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library(HH)
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library(dplyr)
library(modelr)
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library(glmulti)
package ‘glmulti’ was built under R version 3.6.2Loading required package: rJava
package ‘rJava’ was built under R version 3.6.2
avacado <- read.csv("data/avocado.csv") %>% clean_names()
head(avacado)
avacado2 <- avacado %>% 
    dplyr::select(-c("date", "region", "x"))
head(avacado2)
regsubsets_forward <- regsubsets(average_price ~ ., data = avacado2, nvmax = 10, method = "forward")
sum_regsubsets_forward <- summary(regsubsets_forward)
sum_regsubsets_forward
Subset selection object
Call: regsubsets.formula(average_price ~ ., data = avacado2, nvmax = 10, 
    method = "forward")
10 Variables  (and intercept)
             Forced in Forced out
total_volume     FALSE      FALSE
x4046            FALSE      FALSE
x4225            FALSE      FALSE
x4770            FALSE      FALSE
total_bags       FALSE      FALSE
small_bags       FALSE      FALSE
large_bags       FALSE      FALSE
x_large_bags     FALSE      FALSE
typeorganic      FALSE      FALSE
year             FALSE      FALSE
1 subsets of each size up to 10
Selection Algorithm: forward
          total_volume x4046 x4225 x4770 total_bags small_bags large_bags x_large_bags
1  ( 1 )  " "          " "   " "   " "   " "        " "        " "        " "         
2  ( 1 )  " "          " "   " "   " "   " "        " "        " "        " "         
3  ( 1 )  " "          "*"   " "   " "   " "        " "        " "        " "         
4  ( 1 )  " "          "*"   "*"   " "   " "        " "        " "        " "         
5  ( 1 )  " "          "*"   "*"   "*"   " "        " "        " "        " "         
6  ( 1 )  " "          "*"   "*"   "*"   " "        " "        " "        "*"         
7  ( 1 )  " "          "*"   "*"   "*"   " "        " "        "*"        "*"         
8  ( 1 )  " "          "*"   "*"   "*"   "*"        " "        "*"        "*"         
9  ( 1 )  "*"          "*"   "*"   "*"   "*"        " "        "*"        "*"         
10  ( 1 ) "*"          "*"   "*"   "*"   "*"        "*"        "*"        "*"         
          typeorganic year
1  ( 1 )  "*"         " " 
2  ( 1 )  "*"         "*" 
3  ( 1 )  "*"         "*" 
4  ( 1 )  "*"         "*" 
5  ( 1 )  "*"         "*" 
6  ( 1 )  "*"         "*" 
7  ( 1 )  "*"         "*" 
8  ( 1 )  "*"         "*" 
9  ( 1 )  "*"         "*" 
10  ( 1 ) "*"         "*" 

The best predictor model shows us the best predictors using the asterices

# plotting this shows us the adjusted r2 values and which variables are in the model. Top row shows model with highest adjusted r2
plot(regsubsets_forward, scale = "adjr2")

sum_regsubsets_forward$which
   (Intercept) total_volume x4046 x4225 x4770 total_bags small_bags large_bags
1         TRUE        FALSE FALSE FALSE FALSE      FALSE      FALSE      FALSE
2         TRUE        FALSE FALSE FALSE FALSE      FALSE      FALSE      FALSE
3         TRUE        FALSE  TRUE FALSE FALSE      FALSE      FALSE      FALSE
4         TRUE        FALSE  TRUE  TRUE FALSE      FALSE      FALSE      FALSE
5         TRUE        FALSE  TRUE  TRUE  TRUE      FALSE      FALSE      FALSE
6         TRUE        FALSE  TRUE  TRUE  TRUE      FALSE      FALSE      FALSE
7         TRUE        FALSE  TRUE  TRUE  TRUE      FALSE      FALSE       TRUE
8         TRUE        FALSE  TRUE  TRUE  TRUE       TRUE      FALSE       TRUE
9         TRUE         TRUE  TRUE  TRUE  TRUE       TRUE      FALSE       TRUE
10        TRUE         TRUE  TRUE  TRUE  TRUE       TRUE       TRUE       TRUE
   x_large_bags typeorganic  year
1         FALSE        TRUE FALSE
2         FALSE        TRUE  TRUE
3         FALSE        TRUE  TRUE
4         FALSE        TRUE  TRUE
5         FALSE        TRUE  TRUE
6          TRUE        TRUE  TRUE
7          TRUE        TRUE  TRUE
8          TRUE        TRUE  TRUE
9          TRUE        TRUE  TRUE
10         TRUE        TRUE  TRUE
regsubsets_backward <- regsubsets(average_price ~ ., data = avacado2, nvmax = 10, method = "backward")

# plotting this shows us the adjusted r2 values and which variables are in the model. Top row shows model with highest adjusted r2
plot(regsubsets_backward, scale = "adjr2")

regsubsets_exhaustive <- regsubsets(average_price ~ ., data = avacado2, nvmax = 10, method = "exhaustive")

# plotting this shows us the adjusted r2 values and which variables are in the model. Top row shows model with highest adjusted r2
plot(regsubsets_exhaustive, scale = "adjr2")

summary(regsubsets_exhaustive)$which[10,]
 (Intercept) total_volume        x4046        x4225        x4770   total_bags 
        TRUE         TRUE         TRUE         TRUE         TRUE         TRUE 
  small_bags   large_bags x_large_bags  typeorganic         year 
        TRUE         TRUE         TRUE         TRUE         TRUE 
summary(regsubsets_backward)$which[10,]
 (Intercept) total_volume        x4046        x4225        x4770   total_bags 
        TRUE         TRUE         TRUE         TRUE         TRUE         TRUE 
  small_bags   large_bags x_large_bags  typeorganic         year 
        TRUE         TRUE         TRUE         TRUE         TRUE 
summary(regsubsets_forward)$which[10,]
 (Intercept) total_volume        x4046        x4225        x4770   total_bags 
        TRUE         TRUE         TRUE         TRUE         TRUE         TRUE 
  small_bags   large_bags x_large_bags  typeorganic         year 
        TRUE         TRUE         TRUE         TRUE         TRUE 
avacado2 %>%
  ggplot(aes(x = average_price)) +
  geom_histogram()

avacado2 %>%
  ggplot(aes(x = log10(average_price))) +
  geom_histogram()

CODECLAN- SOLUTION

avocados <- clean_names(read_csv("data/avocado.csv"))
Missing column names filled in: 'X1' [1]Parsed with column specification:
cols(
  X1 = col_double(),
  Date = col_date(format = ""),
  AveragePrice = col_double(),
  `Total Volume` = col_double(),
  `4046` = col_double(),
  `4225` = col_double(),
  `4770` = col_double(),
  `Total Bags` = col_double(),
  `Small Bags` = col_double(),
  `Large Bags` = col_double(),
  `XLarge Bags` = col_double(),
  type = col_character(),
  year = col_double(),
  region = col_character()
)

summary(avocados)
       x1             date            average_price    total_volume     
 Min.   : 0.00   Min.   :2015-01-04   Min.   :0.440   Min.   :      85  
 1st Qu.:10.00   1st Qu.:2015-10-25   1st Qu.:1.100   1st Qu.:   10839  
 Median :24.00   Median :2016-08-14   Median :1.370   Median :  107377  
 Mean   :24.23   Mean   :2016-08-13   Mean   :1.406   Mean   :  850644  
 3rd Qu.:38.00   3rd Qu.:2017-06-04   3rd Qu.:1.660   3rd Qu.:  432962  
 Max.   :52.00   Max.   :2018-03-25   Max.   :3.250   Max.   :62505647  
     x4046              x4225              x4770           total_bags      
 Min.   :       0   Min.   :       0   Min.   :      0   Min.   :       0  
 1st Qu.:     854   1st Qu.:    3009   1st Qu.:      0   1st Qu.:    5089  
 Median :    8645   Median :   29061   Median :    185   Median :   39744  
 Mean   :  293008   Mean   :  295155   Mean   :  22840   Mean   :  239639  
 3rd Qu.:  111020   3rd Qu.:  150207   3rd Qu.:   6243   3rd Qu.:  110783  
 Max.   :22743616   Max.   :20470573   Max.   :2546439   Max.   :19373134  
   small_bags         large_bags       x_large_bags          type          
 Min.   :       0   Min.   :      0   Min.   :     0.0   Length:18249      
 1st Qu.:    2849   1st Qu.:    127   1st Qu.:     0.0   Class :character  
 Median :   26363   Median :   2648   Median :     0.0   Mode  :character  
 Mean   :  182195   Mean   :  54338   Mean   :  3106.4                     
 3rd Qu.:   83338   3rd Qu.:  22029   3rd Qu.:   132.5                     
 Max.   :13384587   Max.   :5719097   Max.   :551693.7                     
      year         region         
 Min.   :2015   Length:18249      
 1st Qu.:2015   Class :character  
 Median :2016   Mode  :character  
 Mean   :2016                     
 3rd Qu.:2017                     
 Max.   :2018                     
head(avocados)
avocados %>%
  distinct(region) %>%
  summarise(number_of_regions = n())
avocados %>%
  distinct(date) %>%
  summarise(
    number_of_dates = n(),
    min_date = min(date),
    max_date = max(date)
  )
NA
library(lubridate)
package ‘lubridate’ was built under R version 3.6.2
Attaching package: ‘lubridate’

The following object is masked from ‘package:HH’:

    interval

The following objects are masked from ‘package:base’:

    date, intersect, setdiff, union
trimmed_avocados <- avocados %>%
  mutate(
    quarter = as_factor(quarter(date)),
    year = as_factor(year),
    type = as_factor(type)
  ) %>%
  dplyr::select(-c("x1", "date"))
alias(average_price ~ ., data = trimmed_avocados )
Model :
average_price ~ total_volume + x4046 + x4225 + x4770 + total_bags + 
    small_bags + large_bags + x_large_bags + type + year + region + 
    quarter
trimmed_avocados %>%
  dplyr::select(-region) %>%
  ggpairs()

ggsave("pairs_plot_choice1.png", width = 10, height = 10, units = "in")
trimmed_avocados %>%
  ggplot(aes(x = region, y = average_price)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))

Test competing models with x4046, type, year, quarter and region:

model1a <- lm(average_price ~ x4046, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1a)

summary(model1a)

Call:
lm(formula = average_price ~ x4046, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.98539 -0.29842 -0.03531  0.25459  1.82475 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.425e+00  2.993e-03  476.29   <2e-16 ***
x4046       -6.631e-08  2.305e-09  -28.77   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3939 on 18247 degrees of freedom
Multiple R-squared:  0.0434,    Adjusted R-squared:  0.04334 
F-statistic: 827.8 on 1 and 18247 DF,  p-value: < 2.2e-16
model1b <- lm(average_price ~ type, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1b)

summary(model1b)

Call:
lm(formula = average_price ~ type, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.21400 -0.20400 -0.02804  0.18600  1.59600 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1.158040   0.003321   348.7   <2e-16 ***
typeorganic 0.495959   0.004697   105.6   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3173 on 18247 degrees of freedom
Multiple R-squared:  0.3793,    Adjusted R-squared:  0.3792 
F-statistic: 1.115e+04 on 1 and 18247 DF,  p-value: < 2.2e-16
model1c <- lm(average_price ~ year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1c)

summary(model1c)

Call:
lm(formula = average_price ~ year, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.07513 -0.29513 -0.03559  0.25247  1.91136 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.375590   0.005280 260.546  < 2e-16 ***
year2016    -0.036951   0.007466  -4.949 7.52e-07 ***
year2017     0.139537   0.007432  18.776  < 2e-16 ***
year2018    -0.028060   0.012192  -2.301   0.0214 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3956 on 18245 degrees of freedom
Multiple R-squared:  0.03489,   Adjusted R-squared:  0.03474 
F-statistic: 219.9 on 3 and 18245 DF,  p-value: < 2.2e-16
model1d <- lm(average_price ~ quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1d)

summary(model1d)

Call:
lm(formula = average_price ~ quarter, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.96859 -0.30503 -0.02859  0.25497  1.79497 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1.306605   0.005316 245.769   <2e-16 ***
quarter2    0.068428   0.008077   8.472   <2e-16 ***
quarter3    0.206308   0.008076  25.545   <2e-16 ***
quarter4    0.151983   0.008019  18.952   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3946 on 18245 degrees of freedom
Multiple R-squared:  0.04006,   Adjusted R-squared:  0.03991 
F-statistic: 253.8 on 3 and 18245 DF,  p-value: < 2.2e-16
model1e <- lm(average_price ~ region, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1e)

summary(model1e)

Call:
lm(formula = average_price ~ region, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.97095 -0.28423 -0.03432  0.25207  1.76115 

Coefficients:
                           Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.561036   0.020006  78.029  < 2e-16 ***
regionAtlanta             -0.223077   0.028293  -7.885 3.33e-15 ***
regionBaltimoreWashington -0.026805   0.028293  -0.947  0.34344    
regionBoise               -0.212899   0.028293  -7.525 5.52e-14 ***
regionBoston              -0.030148   0.028293  -1.066  0.28663    
regionBuffaloRochester    -0.044201   0.028293  -1.562  0.11824    
regionCalifornia          -0.165710   0.028293  -5.857 4.79e-09 ***
regionCharlotte            0.045000   0.028293   1.591  0.11173    
regionChicago             -0.004260   0.028293  -0.151  0.88031    
regionCincinnatiDayton    -0.351834   0.028293 -12.436  < 2e-16 ***
regionColumbus            -0.308254   0.028293 -10.895  < 2e-16 ***
regionDallasFtWorth       -0.475444   0.028293 -16.805  < 2e-16 ***
regionDenver              -0.342456   0.028293 -12.104  < 2e-16 ***
regionDetroit             -0.284941   0.028293 -10.071  < 2e-16 ***
regionGrandRapids         -0.056036   0.028293  -1.981  0.04765 *  
regionGreatLakes          -0.222485   0.028293  -7.864 3.94e-15 ***
regionHarrisburgScranton  -0.047751   0.028293  -1.688  0.09147 .  
regionHartfordSpringfield  0.257604   0.028293   9.105  < 2e-16 ***
regionHouston             -0.513107   0.028293 -18.136  < 2e-16 ***
regionIndianapolis        -0.247041   0.028293  -8.732  < 2e-16 ***
regionJacksonville        -0.050089   0.028293  -1.770  0.07668 .  
regionLasVegas            -0.180118   0.028293  -6.366 1.98e-10 ***
regionLosAngeles          -0.345030   0.028293 -12.195  < 2e-16 ***
regionLouisville          -0.274349   0.028293  -9.697  < 2e-16 ***
regionMiamiFtLauderdale   -0.132544   0.028293  -4.685 2.82e-06 ***
regionMidsouth            -0.156272   0.028293  -5.523 3.37e-08 ***
regionNashville           -0.348935   0.028293 -12.333  < 2e-16 ***
regionNewOrleansMobile    -0.256243   0.028293  -9.057  < 2e-16 ***
regionNewYork              0.166538   0.028293   5.886 4.02e-09 ***
regionNortheast            0.040888   0.028293   1.445  0.14843    
regionNorthernNewEngland  -0.083639   0.028293  -2.956  0.00312 ** 
regionOrlando             -0.054822   0.028293  -1.938  0.05268 .  
regionPhiladelphia         0.071095   0.028293   2.513  0.01199 *  
regionPhoenixTucson       -0.336598   0.028293 -11.897  < 2e-16 ***
regionPittsburgh          -0.196716   0.028293  -6.953 3.70e-12 ***
regionPlains              -0.124527   0.028293  -4.401 1.08e-05 ***
regionPortland            -0.243314   0.028293  -8.600  < 2e-16 ***
regionRaleighGreensboro   -0.005917   0.028293  -0.209  0.83434    
regionRichmondNorfolk     -0.269704   0.028293  -9.533  < 2e-16 ***
regionRoanoke             -0.313107   0.028293 -11.067  < 2e-16 ***
regionSacramento           0.060533   0.028293   2.140  0.03241 *  
regionSanDiego            -0.162870   0.028293  -5.757 8.72e-09 ***
regionSanFrancisco         0.243166   0.028293   8.595  < 2e-16 ***
regionSeattle             -0.118462   0.028293  -4.187 2.84e-05 ***
regionSouthCarolina       -0.157751   0.028293  -5.576 2.50e-08 ***
regionSouthCentral        -0.459793   0.028293 -16.251  < 2e-16 ***
regionSoutheast           -0.163018   0.028293  -5.762 8.45e-09 ***
regionSpokane             -0.115444   0.028293  -4.080 4.52e-05 ***
regionStLouis             -0.130414   0.028293  -4.609 4.06e-06 ***
regionSyracuse            -0.040710   0.028293  -1.439  0.15020    
regionTampa               -0.152189   0.028293  -5.379 7.58e-08 ***
regionTotalUS             -0.242012   0.028293  -8.554  < 2e-16 ***
regionWest                -0.288817   0.028293 -10.208  < 2e-16 ***
regionWestTexNewMexico    -0.299334   0.028356 -10.556  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3678 on 18195 degrees of freedom
Multiple R-squared:  0.1681,    Adjusted R-squared:  0.1657 
F-statistic: 69.38 on 53 and 18195 DF,  p-value: < 2.2e-16

model1b with type is best, so we’ll keep that and re-run ggpairs() with the residuals (again omitting region).

avocados_remaining_resid <- trimmed_avocados %>%
  add_residuals(model1b) %>%
  dplyr::select(-c("average_price", "type", "region"))

ggpairs(avocados_remaining_resid)

ggsave("pairs_plot_choice2.png", width = 10, height = 10, units = "in")
trimmed_avocados %>%
  add_residuals(model1b) %>%
  ggplot(aes(x = region, y = resid)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))

Looks like x4046, year, quarter and region are our next strong contenders:

model2a <- lm(average_price ~ type + x4046, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model2a)

summary(model2a)

Call:
lm(formula = average_price ~ type + x4046, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.21416 -0.20029 -0.02736  0.18591  1.59589 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.171e+00  3.485e-03  336.13   <2e-16 ***
typeorganic  4.827e-01  4.802e-03  100.52   <2e-16 ***
x4046       -2.323e-08  1.898e-09  -12.24   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.316 on 18246 degrees of freedom
Multiple R-squared:  0.3843,    Adjusted R-squared:  0.3843 
F-statistic:  5695 on 2 and 18246 DF,  p-value: < 2.2e-16
model2b <- lm(average_price ~ type + year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model2b)

summary(model2b)

Call:
lm(formula = average_price ~ type + year, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.32320 -0.18722 -0.01722  0.18278  1.66337 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.127645   0.004704 239.735  < 2e-16 ***
typeorganic  0.495980   0.004563 108.685  < 2e-16 ***
year2016    -0.036995   0.005817  -6.360 2.07e-10 ***
year2017     0.139580   0.005790  24.107  < 2e-16 ***
year2018    -0.028104   0.009499  -2.959  0.00309 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3082 on 18244 degrees of freedom
Multiple R-squared:  0.4142,    Adjusted R-squared:  0.4141 
F-statistic:  3225 on 4 and 18244 DF,  p-value: < 2.2e-16
model2c <- lm(average_price ~ type + quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model2c)

summary(model2c)

Call:
lm(formula = average_price ~ type + quarter, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.11458 -0.20089 -0.02458  0.18542  1.54687 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1.058626   0.004718  224.38   <2e-16 ***
typeorganic 0.495958   0.004543  109.16   <2e-16 ***
quarter2    0.068546   0.006282   10.91   <2e-16 ***
quarter3    0.206308   0.006281   32.84   <2e-16 ***
quarter4    0.152040   0.006237   24.38   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3069 on 18244 degrees of freedom
Multiple R-squared:  0.4193,    Adjusted R-squared:  0.4192 
F-statistic:  3294 on 4 and 18244 DF,  p-value: < 2.2e-16
model2d <- lm(average_price ~ type + region, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model2d)

summary(model2d)

Call:
lm(formula = average_price ~ type + region, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.09858 -0.16716 -0.01814  0.14692  1.51320 

Coefficients:
                           Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.313079   0.014894  88.159  < 2e-16 ***
typeorganic                0.495912   0.004017 123.452  < 2e-16 ***
regionAtlanta             -0.223077   0.020871 -10.688  < 2e-16 ***
regionBaltimoreWashington -0.026805   0.020871  -1.284  0.19906    
regionBoise               -0.212899   0.020871 -10.201  < 2e-16 ***
regionBoston              -0.030148   0.020871  -1.444  0.14863    
regionBuffaloRochester    -0.044201   0.020871  -2.118  0.03421 *  
regionCalifornia          -0.165710   0.020871  -7.940 2.15e-15 ***
regionCharlotte            0.045000   0.020871   2.156  0.03109 *  
regionChicago             -0.004260   0.020871  -0.204  0.83826    
regionCincinnatiDayton    -0.351834   0.020871 -16.857  < 2e-16 ***
regionColumbus            -0.308254   0.020871 -14.769  < 2e-16 ***
regionDallasFtWorth       -0.475444   0.020871 -22.780  < 2e-16 ***
regionDenver              -0.342456   0.020871 -16.408  < 2e-16 ***
regionDetroit             -0.284941   0.020871 -13.652  < 2e-16 ***
regionGrandRapids         -0.056036   0.020871  -2.685  0.00726 ** 
regionGreatLakes          -0.222485   0.020871 -10.660  < 2e-16 ***
regionHarrisburgScranton  -0.047751   0.020871  -2.288  0.02216 *  
regionHartfordSpringfield  0.257604   0.020871  12.342  < 2e-16 ***
regionHouston             -0.513107   0.020871 -24.584  < 2e-16 ***
regionIndianapolis        -0.247041   0.020871 -11.836  < 2e-16 ***
regionJacksonville        -0.050089   0.020871  -2.400  0.01641 *  
regionLasVegas            -0.180118   0.020871  -8.630  < 2e-16 ***
regionLosAngeles          -0.345030   0.020871 -16.531  < 2e-16 ***
regionLouisville          -0.274349   0.020871 -13.145  < 2e-16 ***
regionMiamiFtLauderdale   -0.132544   0.020871  -6.351 2.20e-10 ***
regionMidsouth            -0.156272   0.020871  -7.487 7.35e-14 ***
regionNashville           -0.348935   0.020871 -16.718  < 2e-16 ***
regionNewOrleansMobile    -0.256243   0.020871 -12.277  < 2e-16 ***
regionNewYork              0.166538   0.020871   7.979 1.56e-15 ***
regionNortheast            0.040888   0.020871   1.959  0.05013 .  
regionNorthernNewEngland  -0.083639   0.020871  -4.007 6.16e-05 ***
regionOrlando             -0.054822   0.020871  -2.627  0.00863 ** 
regionPhiladelphia         0.071095   0.020871   3.406  0.00066 ***
regionPhoenixTucson       -0.336598   0.020871 -16.127  < 2e-16 ***
regionPittsburgh          -0.196716   0.020871  -9.425  < 2e-16 ***
regionPlains              -0.124527   0.020871  -5.966 2.47e-09 ***
regionPortland            -0.243314   0.020871 -11.658  < 2e-16 ***
regionRaleighGreensboro   -0.005917   0.020871  -0.284  0.77679    
regionRichmondNorfolk     -0.269704   0.020871 -12.922  < 2e-16 ***
regionRoanoke             -0.313107   0.020871 -15.002  < 2e-16 ***
regionSacramento           0.060533   0.020871   2.900  0.00373 ** 
regionSanDiego            -0.162870   0.020871  -7.803 6.35e-15 ***
regionSanFrancisco         0.243166   0.020871  11.651  < 2e-16 ***
regionSeattle             -0.118462   0.020871  -5.676 1.40e-08 ***
regionSouthCarolina       -0.157751   0.020871  -7.558 4.28e-14 ***
regionSouthCentral        -0.459793   0.020871 -22.030  < 2e-16 ***
regionSoutheast           -0.163018   0.020871  -7.811 6.00e-15 ***
regionSpokane             -0.115444   0.020871  -5.531 3.22e-08 ***
regionStLouis             -0.130414   0.020871  -6.248 4.24e-10 ***
regionSyracuse            -0.040710   0.020871  -1.951  0.05113 .  
regionTampa               -0.152189   0.020871  -7.292 3.18e-13 ***
regionTotalUS             -0.242012   0.020871 -11.595  < 2e-16 ***
regionWest                -0.288817   0.020871 -13.838  < 2e-16 ***
regionWestTexNewMexico    -0.297114   0.020918 -14.204  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2713 on 18194 degrees of freedom
Multiple R-squared:  0.5473,    Adjusted R-squared:  0.546 
F-statistic: 407.4 on 54 and 18194 DF,  p-value: < 2.2e-16

So model2d with type and region comes out as better here. We have some region coefficients that are not significant at 0.05 level, so let’s run an anova() to test whether to include region

anova(model1b, model2d)
Analysis of Variance Table

Model 1: average_price ~ type
Model 2: average_price ~ type + region
  Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
1  18247 1836.7                                  
2  18194 1339.4 53    497.26 127.44 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

It seems region is significant overall, so we’ll keep it in!

avocados_remaining_resid <- trimmed_avocados %>%
  add_residuals(model2d) %>%
  dplyr::select(-c("average_price", "type", "region"))

ggpairs(avocados_remaining_resid)

ggsave("pairs_plot_choice3.png", width = 10, height = 10, units = "in")
model3a <- lm(average_price ~ type + region + x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model3a)

summary(model3a)

Call:
lm(formula = average_price ~ type + region + x_large_bags, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.10024 -0.16726 -0.01734  0.14591  1.51156 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.311e+00  1.489e-02  88.033  < 2e-16 ***
typeorganic                5.001e-01  4.101e-03 121.953  < 2e-16 ***
regionAtlanta             -2.235e-01  2.086e-02 -10.718  < 2e-16 ***
regionBaltimoreWashington -2.713e-02  2.086e-02  -1.301 0.193298    
regionBoise               -2.128e-01  2.086e-02 -10.204  < 2e-16 ***
regionBoston              -3.023e-02  2.086e-02  -1.449 0.147234    
regionBuffaloRochester    -4.428e-02  2.086e-02  -2.123 0.033774 *  
regionCalifornia          -1.762e-01  2.096e-02  -8.408  < 2e-16 ***
regionCharlotte            4.495e-02  2.086e-02   2.155 0.031177 *  
regionChicago             -4.936e-03  2.086e-02  -0.237 0.812924    
regionCincinnatiDayton    -3.523e-01  2.086e-02 -16.890  < 2e-16 ***
regionColumbus            -3.086e-01  2.086e-02 -14.796  < 2e-16 ***
regionDallasFtWorth       -4.762e-01  2.086e-02 -22.832  < 2e-16 ***
regionDenver              -3.425e-01  2.086e-02 -16.420  < 2e-16 ***
regionDetroit             -2.882e-01  2.087e-02 -13.810  < 2e-16 ***
regionGrandRapids         -5.764e-02  2.086e-02  -2.763 0.005731 ** 
regionGreatLakes          -2.353e-01  2.101e-02 -11.198  < 2e-16 ***
regionHarrisburgScranton  -4.798e-02  2.086e-02  -2.300 0.021451 *  
regionHartfordSpringfield  2.575e-01  2.086e-02  12.347  < 2e-16 ***
regionHouston             -5.137e-01  2.086e-02 -24.628  < 2e-16 ***
regionIndianapolis        -2.475e-01  2.086e-02 -11.867  < 2e-16 ***
regionJacksonville        -5.021e-02  2.086e-02  -2.407 0.016074 *  
regionLasVegas            -1.801e-01  2.086e-02  -8.633  < 2e-16 ***
regionLosAngeles          -3.532e-01  2.092e-02 -16.881  < 2e-16 ***
regionLouisville          -2.745e-01  2.086e-02 -13.160  < 2e-16 ***
regionMiamiFtLauderdale   -1.331e-01  2.086e-02  -6.380 1.81e-10 ***
regionMidsouth            -1.590e-01  2.086e-02  -7.619 2.68e-14 ***
regionNashville           -3.491e-01  2.086e-02 -16.736  < 2e-16 ***
regionNewOrleansMobile    -2.572e-01  2.086e-02 -12.330  < 2e-16 ***
regionNewYork              1.659e-01  2.086e-02   7.954 1.91e-15 ***
regionNortheast            3.834e-02  2.086e-02   1.838 0.066151 .  
regionNorthernNewEngland  -8.377e-02  2.086e-02  -4.017 5.93e-05 ***
regionOrlando             -5.523e-02  2.086e-02  -2.648 0.008111 ** 
regionPhiladelphia         7.097e-02  2.086e-02   3.403 0.000669 ***
regionPhoenixTucson       -3.368e-01  2.086e-02 -16.149  < 2e-16 ***
regionPittsburgh          -1.967e-01  2.086e-02  -9.433  < 2e-16 ***
regionPlains              -1.267e-01  2.086e-02  -6.072 1.29e-09 ***
regionPortland            -2.434e-01  2.086e-02 -11.669  < 2e-16 ***
regionRaleighGreensboro   -6.021e-03  2.086e-02  -0.289 0.772828    
regionRichmondNorfolk     -2.699e-01  2.086e-02 -12.939  < 2e-16 ***
regionRoanoke             -3.132e-01  2.086e-02 -15.015  < 2e-16 ***
regionSacramento           6.020e-02  2.086e-02   2.886 0.003904 ** 
regionSanDiego            -1.631e-01  2.086e-02  -7.819 5.64e-15 ***
regionSanFrancisco         2.428e-01  2.086e-02  11.642  < 2e-16 ***
regionSeattle             -1.185e-01  2.086e-02  -5.682 1.35e-08 ***
regionSouthCarolina       -1.581e-01  2.086e-02  -7.581 3.59e-14 ***
regionSouthCentral        -4.650e-01  2.088e-02 -22.268  < 2e-16 ***
regionSoutheast           -1.680e-01  2.088e-02  -8.046 9.10e-16 ***
regionSpokane             -1.154e-01  2.086e-02  -5.531 3.22e-08 ***
regionStLouis             -1.308e-01  2.086e-02  -6.270 3.69e-10 ***
regionSyracuse            -4.071e-02  2.086e-02  -1.952 0.050993 .  
regionTampa               -1.526e-01  2.086e-02  -7.315 2.68e-13 ***
regionTotalUS             -2.852e-01  2.255e-02 -12.648  < 2e-16 ***
regionWest                -2.904e-01  2.086e-02 -13.922  < 2e-16 ***
regionWestTexNewMexico    -2.976e-01  2.090e-02 -14.238  < 2e-16 ***
x_large_bags               6.810e-07  1.351e-07   5.040 4.70e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2711 on 18193 degrees of freedom
Multiple R-squared:  0.548, Adjusted R-squared:  0.5466 
F-statistic:   401 on 55 and 18193 DF,  p-value: < 2.2e-16
model3b <- lm(average_price ~ type + region + year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model3b)

summary(model3b)

Call:
lm(formula = average_price ~ type + region + year, data = trimmed_avocados)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.1532 -0.1497 -0.0060  0.1419  1.4849 

Coefficients:
                           Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.282672   0.014600  87.857  < 2e-16 ***
typeorganic                0.495933   0.003859 128.501  < 2e-16 ***
regionAtlanta             -0.223077   0.020052 -11.125  < 2e-16 ***
regionBaltimoreWashington -0.026805   0.020052  -1.337 0.181322    
regionBoise               -0.212899   0.020052 -10.617  < 2e-16 ***
regionBoston              -0.030148   0.020052  -1.503 0.132735    
regionBuffaloRochester    -0.044201   0.020052  -2.204 0.027515 *  
regionCalifornia          -0.165710   0.020052  -8.264  < 2e-16 ***
regionCharlotte            0.045000   0.020052   2.244 0.024835 *  
regionChicago             -0.004260   0.020052  -0.212 0.831748    
regionCincinnatiDayton    -0.351834   0.020052 -17.546  < 2e-16 ***
regionColumbus            -0.308254   0.020052 -15.373  < 2e-16 ***
regionDallasFtWorth       -0.475444   0.020052 -23.710  < 2e-16 ***
regionDenver              -0.342456   0.020052 -17.078  < 2e-16 ***
regionDetroit             -0.284941   0.020052 -14.210  < 2e-16 ***
regionGrandRapids         -0.056036   0.020052  -2.794 0.005204 ** 
regionGreatLakes          -0.222485   0.020052 -11.095  < 2e-16 ***
regionHarrisburgScranton  -0.047751   0.020052  -2.381 0.017259 *  
regionHartfordSpringfield  0.257604   0.020052  12.847  < 2e-16 ***
regionHouston             -0.513107   0.020052 -25.589  < 2e-16 ***
regionIndianapolis        -0.247041   0.020052 -12.320  < 2e-16 ***
regionJacksonville        -0.050089   0.020052  -2.498 0.012501 *  
regionLasVegas            -0.180118   0.020052  -8.982  < 2e-16 ***
regionLosAngeles          -0.345030   0.020052 -17.207  < 2e-16 ***
regionLouisville          -0.274349   0.020052 -13.682  < 2e-16 ***
regionMiamiFtLauderdale   -0.132544   0.020052  -6.610 3.95e-11 ***
regionMidsouth            -0.156272   0.020052  -7.793 6.88e-15 ***
regionNashville           -0.348935   0.020052 -17.401  < 2e-16 ***
regionNewOrleansMobile    -0.256243   0.020052 -12.779  < 2e-16 ***
regionNewYork              0.166538   0.020052   8.305  < 2e-16 ***
regionNortheast            0.040888   0.020052   2.039 0.041459 *  
regionNorthernNewEngland  -0.083639   0.020052  -4.171 3.05e-05 ***
regionOrlando             -0.054822   0.020052  -2.734 0.006263 ** 
regionPhiladelphia         0.071095   0.020052   3.545 0.000393 ***
regionPhoenixTucson       -0.336598   0.020052 -16.786  < 2e-16 ***
regionPittsburgh          -0.196716   0.020052  -9.810  < 2e-16 ***
regionPlains              -0.124527   0.020052  -6.210 5.41e-10 ***
regionPortland            -0.243314   0.020052 -12.134  < 2e-16 ***
regionRaleighGreensboro   -0.005917   0.020052  -0.295 0.767930    
regionRichmondNorfolk     -0.269704   0.020052 -13.450  < 2e-16 ***
regionRoanoke             -0.313107   0.020052 -15.615  < 2e-16 ***
regionSacramento           0.060533   0.020052   3.019 0.002542 ** 
regionSanDiego            -0.162870   0.020052  -8.122 4.86e-16 ***
regionSanFrancisco         0.243166   0.020052  12.127  < 2e-16 ***
regionSeattle             -0.118462   0.020052  -5.908 3.53e-09 ***
regionSouthCarolina       -0.157751   0.020052  -7.867 3.83e-15 ***
regionSouthCentral        -0.459793   0.020052 -22.930  < 2e-16 ***
regionSoutheast           -0.163018   0.020052  -8.130 4.58e-16 ***
regionSpokane             -0.115444   0.020052  -5.757 8.69e-09 ***
regionStLouis             -0.130414   0.020052  -6.504 8.04e-11 ***
regionSyracuse            -0.040710   0.020052  -2.030 0.042350 *  
regionTampa               -0.152189   0.020052  -7.590 3.36e-14 ***
regionTotalUS             -0.242012   0.020052 -12.069  < 2e-16 ***
regionWest                -0.288817   0.020052 -14.403  < 2e-16 ***
regionWestTexNewMexico    -0.296552   0.020097 -14.756  < 2e-16 ***
year2016                  -0.036970   0.004920  -7.515 5.96e-14 ***
year2017                   0.139555   0.004897  28.500  < 2e-16 ***
year2018                  -0.028078   0.008033  -3.495 0.000475 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2607 on 18191 degrees of freedom
Multiple R-squared:  0.5822,    Adjusted R-squared:  0.5809 
F-statistic: 444.8 on 57 and 18191 DF,  p-value: < 2.2e-16
model3c <- lm(average_price ~ type + region + quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model3c)

summary(model3c)

Call:
lm(formula = average_price ~ type + region + quarter, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.06767 -0.15971 -0.01185  0.14629  1.54411 

Coefficients:
                           Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.213689   0.014517  83.603  < 2e-16 ***
typeorganic                0.495911   0.003835 129.296  < 2e-16 ***
regionAtlanta             -0.223077   0.019928 -11.194  < 2e-16 ***
regionBaltimoreWashington -0.026805   0.019928  -1.345 0.178619    
regionBoise               -0.212899   0.019928 -10.683  < 2e-16 ***
regionBoston              -0.030148   0.019928  -1.513 0.130339    
regionBuffaloRochester    -0.044201   0.019928  -2.218 0.026565 *  
regionCalifornia          -0.165710   0.019928  -8.315  < 2e-16 ***
regionCharlotte            0.045000   0.019928   2.258 0.023950 *  
regionChicago             -0.004260   0.019928  -0.214 0.830716    
regionCincinnatiDayton    -0.351834   0.019928 -17.655  < 2e-16 ***
regionColumbus            -0.308254   0.019928 -15.468  < 2e-16 ***
regionDallasFtWorth       -0.475444   0.019928 -23.858  < 2e-16 ***
regionDenver              -0.342456   0.019928 -17.185  < 2e-16 ***
regionDetroit             -0.284941   0.019928 -14.298  < 2e-16 ***
regionGrandRapids         -0.056036   0.019928  -2.812 0.004931 ** 
regionGreatLakes          -0.222485   0.019928 -11.164  < 2e-16 ***
regionHarrisburgScranton  -0.047751   0.019928  -2.396 0.016577 *  
regionHartfordSpringfield  0.257604   0.019928  12.927  < 2e-16 ***
regionHouston             -0.513107   0.019928 -25.748  < 2e-16 ***
regionIndianapolis        -0.247041   0.019928 -12.397  < 2e-16 ***
regionJacksonville        -0.050089   0.019928  -2.513 0.011963 *  
regionLasVegas            -0.180118   0.019928  -9.038  < 2e-16 ***
regionLosAngeles          -0.345030   0.019928 -17.314  < 2e-16 ***
regionLouisville          -0.274349   0.019928 -13.767  < 2e-16 ***
regionMiamiFtLauderdale   -0.132544   0.019928  -6.651 2.99e-11 ***
regionMidsouth            -0.156272   0.019928  -7.842 4.69e-15 ***
regionNashville           -0.348935   0.019928 -17.510  < 2e-16 ***
regionNewOrleansMobile    -0.256243   0.019928 -12.858  < 2e-16 ***
regionNewYork              0.166538   0.019928   8.357  < 2e-16 ***
regionNortheast            0.040888   0.019928   2.052 0.040208 *  
regionNorthernNewEngland  -0.083639   0.019928  -4.197 2.72e-05 ***
regionOrlando             -0.054822   0.019928  -2.751 0.005947 ** 
regionPhiladelphia         0.071095   0.019928   3.568 0.000361 ***
regionPhoenixTucson       -0.336598   0.019928 -16.891  < 2e-16 ***
regionPittsburgh          -0.196716   0.019928  -9.871  < 2e-16 ***
regionPlains              -0.124527   0.019928  -6.249 4.23e-10 ***
regionPortland            -0.243314   0.019928 -12.210  < 2e-16 ***
regionRaleighGreensboro   -0.005917   0.019928  -0.297 0.766527    
regionRichmondNorfolk     -0.269704   0.019928 -13.534  < 2e-16 ***
regionRoanoke             -0.313107   0.019928 -15.712  < 2e-16 ***
regionSacramento           0.060533   0.019928   3.038 0.002389 ** 
regionSanDiego            -0.162870   0.019928  -8.173 3.21e-16 ***
regionSanFrancisco         0.243166   0.019928  12.202  < 2e-16 ***
regionSeattle             -0.118462   0.019928  -5.944 2.82e-09 ***
regionSouthCarolina       -0.157751   0.019928  -7.916 2.59e-15 ***
regionSouthCentral        -0.459793   0.019928 -23.073  < 2e-16 ***
regionSoutheast           -0.163018   0.019928  -8.180 3.02e-16 ***
regionSpokane             -0.115444   0.019928  -5.793 7.03e-09 ***
regionStLouis             -0.130414   0.019928  -6.544 6.14e-11 ***
regionSyracuse            -0.040710   0.019928  -2.043 0.041082 *  
regionTampa               -0.152189   0.019928  -7.637 2.33e-14 ***
regionTotalUS             -0.242012   0.019928 -12.144  < 2e-16 ***
regionWest                -0.288817   0.019928 -14.493  < 2e-16 ***
regionWestTexNewMexico    -0.297141   0.019973 -14.877  < 2e-16 ***
quarter2                   0.068479   0.005303  12.912  < 2e-16 ***
quarter3                   0.206308   0.005303  38.906  < 2e-16 ***
quarter4                   0.152007   0.005265  28.869  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2591 on 18191 degrees of freedom
Multiple R-squared:  0.5874,    Adjusted R-squared:  0.5861 
F-statistic: 454.3 on 57 and 18191 DF,  p-value: < 2.2e-16

So model3c with type, region and quarter wins out here. Everything still looks reasonable with the diagnostics, perhaps some mild heteroscedasticity.

avocados_remaining_resid <- trimmed_avocados %>%
  add_residuals(model3c) %>%
  dplyr::select(-c("average_price", "type", "region", "quarter"))

ggpairs(avocados_remaining_resid)

ggsave("pairs_plot_choice4.png", width = 10, height = 10, units = "in")
model4a <- lm(average_price ~ type + region + quarter + x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model4a)

summary(model4a)

Call:
lm(formula = average_price ~ type + region + quarter + x_large_bags, 
    data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.06889 -0.16013 -0.01154  0.14553  1.54291 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.212e+00  1.451e-02  83.493  < 2e-16 ***
typeorganic                4.998e-01  3.916e-03 127.614  < 2e-16 ***
regionAtlanta             -2.235e-01  1.992e-02 -11.222  < 2e-16 ***
regionBaltimoreWashington -2.711e-02  1.992e-02  -1.361 0.173535    
regionBoise               -2.128e-01  1.992e-02 -10.687  < 2e-16 ***
regionBoston              -3.022e-02  1.992e-02  -1.518 0.129137    
regionBuffaloRochester    -4.427e-02  1.992e-02  -2.223 0.026233 *  
regionCalifornia          -1.753e-01  2.002e-02  -8.759  < 2e-16 ***
regionCharlotte            4.495e-02  1.992e-02   2.257 0.024015 *  
regionChicago             -4.877e-03  1.992e-02  -0.245 0.806549    
regionCincinnatiDayton    -3.522e-01  1.992e-02 -17.686  < 2e-16 ***
regionColumbus            -3.086e-01  1.992e-02 -15.494  < 2e-16 ***
regionDallasFtWorth       -4.762e-01  1.992e-02 -23.908  < 2e-16 ***
regionDenver              -3.425e-01  1.992e-02 -17.196  < 2e-16 ***
regionDetroit             -2.879e-01  1.993e-02 -14.449  < 2e-16 ***
regionGrandRapids         -5.750e-02  1.992e-02  -2.887 0.003898 ** 
regionGreatLakes          -2.342e-01  2.006e-02 -11.671  < 2e-16 ***
regionHarrisburgScranton  -4.796e-02  1.992e-02  -2.408 0.016054 *  
regionHartfordSpringfield  2.575e-01  1.992e-02  12.931  < 2e-16 ***
regionHouston             -5.136e-01  1.992e-02 -25.789  < 2e-16 ***
regionIndianapolis        -2.475e-01  1.992e-02 -12.426  < 2e-16 ***
regionJacksonville        -5.020e-02  1.992e-02  -2.521 0.011720 *  
regionLasVegas            -1.801e-01  1.992e-02  -9.041  < 2e-16 ***
regionLosAngeles          -3.524e-01  1.998e-02 -17.644  < 2e-16 ***
regionLouisville          -2.745e-01  1.992e-02 -13.781  < 2e-16 ***
regionMiamiFtLauderdale   -1.330e-01  1.992e-02  -6.679 2.47e-11 ***
regionMidsouth            -1.587e-01  1.992e-02  -7.967 1.72e-15 ***
regionNashville           -3.491e-01  1.992e-02 -17.527  < 2e-16 ***
regionNewOrleansMobile    -2.571e-01  1.992e-02 -12.909  < 2e-16 ***
regionNewYork              1.660e-01  1.992e-02   8.333  < 2e-16 ***
regionNortheast            3.856e-02  1.992e-02   1.936 0.052939 .  
regionNorthernNewEngland  -8.376e-02  1.992e-02  -4.206 2.61e-05 ***
regionOrlando             -5.519e-02  1.992e-02  -2.771 0.005592 ** 
regionPhiladelphia         7.098e-02  1.992e-02   3.564 0.000366 ***
regionPhoenixTucson       -3.368e-01  1.992e-02 -16.911  < 2e-16 ***
regionPittsburgh          -1.967e-01  1.992e-02  -9.879  < 2e-16 ***
regionPlains              -1.265e-01  1.992e-02  -6.350 2.20e-10 ***
regionPortland            -2.434e-01  1.992e-02 -12.220  < 2e-16 ***
regionRaleighGreensboro   -6.012e-03  1.992e-02  -0.302 0.762753    
regionRichmondNorfolk     -2.699e-01  1.992e-02 -13.549  < 2e-16 ***
regionRoanoke             -3.132e-01  1.992e-02 -15.725  < 2e-16 ***
regionSacramento           6.023e-02  1.992e-02   3.024 0.002497 ** 
regionSanDiego            -1.631e-01  1.992e-02  -8.187 2.85e-16 ***
regionSanFrancisco         2.429e-01  1.992e-02  12.194  < 2e-16 ***
regionSeattle             -1.185e-01  1.992e-02  -5.950 2.72e-09 ***
regionSouthCarolina       -1.581e-01  1.992e-02  -7.938 2.18e-15 ***
regionSouthCentral        -4.646e-01  1.994e-02 -23.297  < 2e-16 ***
regionSoutheast           -1.676e-01  1.994e-02  -8.404  < 2e-16 ***
regionSpokane             -1.154e-01  1.992e-02  -5.793 7.02e-09 ***
regionStLouis             -1.307e-01  1.992e-02  -6.565 5.35e-11 ***
regionSyracuse            -4.071e-02  1.992e-02  -2.044 0.040974 *  
regionTampa               -1.525e-01  1.992e-02  -7.659 1.96e-14 ***
regionTotalUS             -2.814e-01  2.153e-02 -13.068  < 2e-16 ***
regionWest                -2.903e-01  1.992e-02 -14.573  < 2e-16 ***
regionWestTexNewMexico    -2.976e-01  1.996e-02 -14.910  < 2e-16 ***
quarter2                   6.806e-02  5.301e-03  12.839  < 2e-16 ***
quarter3                   2.055e-01  5.302e-03  38.761  < 2e-16 ***
quarter4                   1.527e-01  5.264e-03  29.001  < 2e-16 ***
x_large_bags               6.215e-07  1.292e-07   4.810 1.52e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2589 on 18190 degrees of freedom
Multiple R-squared:  0.5879,    Adjusted R-squared:  0.5866 
F-statistic: 447.4 on 58 and 18190 DF,  p-value: < 2.2e-16
model4b <- lm(average_price ~ type + region + quarter + year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model4b)

summary(model4b)

Call:
lm(formula = average_price ~ type + region + quarter + year, 
    data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.03683 -0.14588 -0.00412  0.14386  1.43930 

Coefficients:
                           Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.167184   0.014290  81.677  < 2e-16 ***
typeorganic                0.495930   0.003675 134.950  < 2e-16 ***
regionAtlanta             -0.223077   0.019094 -11.683  < 2e-16 ***
regionBaltimoreWashington -0.026805   0.019094  -1.404 0.160383    
regionBoise               -0.212899   0.019094 -11.150  < 2e-16 ***
regionBoston              -0.030148   0.019094  -1.579 0.114368    
regionBuffaloRochester    -0.044201   0.019094  -2.315 0.020627 *  
regionCalifornia          -0.165710   0.019094  -8.679  < 2e-16 ***
regionCharlotte            0.045000   0.019094   2.357 0.018445 *  
regionChicago             -0.004260   0.019094  -0.223 0.823439    
regionCincinnatiDayton    -0.351834   0.019094 -18.427  < 2e-16 ***
regionColumbus            -0.308254   0.019094 -16.144  < 2e-16 ***
regionDallasFtWorth       -0.475444   0.019094 -24.900  < 2e-16 ***
regionDenver              -0.342456   0.019094 -17.935  < 2e-16 ***
regionDetroit             -0.284941   0.019094 -14.923  < 2e-16 ***
regionGrandRapids         -0.056036   0.019094  -2.935 0.003342 ** 
regionGreatLakes          -0.222485   0.019094 -11.652  < 2e-16 ***
regionHarrisburgScranton  -0.047751   0.019094  -2.501 0.012397 *  
regionHartfordSpringfield  0.257604   0.019094  13.491  < 2e-16 ***
regionHouston             -0.513107   0.019094 -26.873  < 2e-16 ***
regionIndianapolis        -0.247041   0.019094 -12.938  < 2e-16 ***
regionJacksonville        -0.050089   0.019094  -2.623 0.008716 ** 
regionLasVegas            -0.180118   0.019094  -9.433  < 2e-16 ***
regionLosAngeles          -0.345030   0.019094 -18.070  < 2e-16 ***
regionLouisville          -0.274349   0.019094 -14.368  < 2e-16 ***
regionMiamiFtLauderdale   -0.132544   0.019094  -6.942 4.00e-12 ***
regionMidsouth            -0.156272   0.019094  -8.184 2.91e-16 ***
regionNashville           -0.348935   0.019094 -18.275  < 2e-16 ***
regionNewOrleansMobile    -0.256243   0.019094 -13.420  < 2e-16 ***
regionNewYork              0.166538   0.019094   8.722  < 2e-16 ***
regionNortheast            0.040888   0.019094   2.141 0.032255 *  
regionNorthernNewEngland  -0.083639   0.019094  -4.380 1.19e-05 ***
regionOrlando             -0.054822   0.019094  -2.871 0.004094 ** 
regionPhiladelphia         0.071095   0.019094   3.723 0.000197 ***
regionPhoenixTucson       -0.336598   0.019094 -17.629  < 2e-16 ***
regionPittsburgh          -0.196716   0.019094 -10.303  < 2e-16 ***
regionPlains              -0.124527   0.019094  -6.522 7.13e-11 ***
regionPortland            -0.243314   0.019094 -12.743  < 2e-16 ***
regionRaleighGreensboro   -0.005917   0.019094  -0.310 0.756641    
regionRichmondNorfolk     -0.269704   0.019094 -14.125  < 2e-16 ***
regionRoanoke             -0.313107   0.019094 -16.398  < 2e-16 ***
regionSacramento           0.060533   0.019094   3.170 0.001526 ** 
regionSanDiego            -0.162870   0.019094  -8.530  < 2e-16 ***
regionSanFrancisco         0.243166   0.019094  12.735  < 2e-16 ***
regionSeattle             -0.118462   0.019094  -6.204 5.62e-10 ***
regionSouthCarolina       -0.157751   0.019094  -8.262  < 2e-16 ***
regionSouthCentral        -0.459793   0.019094 -24.081  < 2e-16 ***
regionSoutheast           -0.163018   0.019094  -8.538  < 2e-16 ***
regionSpokane             -0.115444   0.019094  -6.046 1.51e-09 ***
regionStLouis             -0.130414   0.019094  -6.830 8.75e-12 ***
regionSyracuse            -0.040710   0.019094  -2.132 0.033011 *  
regionTampa               -0.152189   0.019094  -7.971 1.67e-15 ***
regionTotalUS             -0.242012   0.019094 -12.675  < 2e-16 ***
regionWest                -0.288817   0.019094 -15.126  < 2e-16 ***
regionWestTexNewMexico    -0.296624   0.019137 -15.500  < 2e-16 ***
quarter2                   0.081121   0.005410  14.996  < 2e-16 ***
quarter3                   0.218901   0.005409  40.471  < 2e-16 ***
quarter4                   0.161972   0.005376  30.130  < 2e-16 ***
year2016                  -0.036978   0.004684  -7.894 3.10e-15 ***
year2017                   0.138658   0.004663  29.735  < 2e-16 ***
year2018                   0.087412   0.008334  10.488  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2482 on 18188 degrees of freedom
Multiple R-squared:  0.6213,    Adjusted R-squared:   0.62 
F-statistic: 497.3 on 60 and 18188 DF,  p-value: < 2.2e-16

Hmm, model4b with type, region, quarter and year wins here

avocados_remaining_resid <- trimmed_avocados %>%
  add_residuals(model4b) %>%
  dplyr::select(-c("average_price", "type", "region", "quarter", "year"))

ggpairs(avocados_remaining_resid)

ggsave("pairs_plot_choice5.png", width = 10, height = 10, units = "in")

It looks like x_large_bags is the remaining contender, let’s check it out!

model5 <- lm(average_price ~ type + region + quarter + year + x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5)

summary(model5)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.03610 -0.14545 -0.00439  0.14420  1.43907 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.167e+00  1.429e-02  81.687  < 2e-16 ***
typeorganic                4.982e-01  3.755e-03 132.674  < 2e-16 ***
regionAtlanta             -2.233e-01  1.909e-02 -11.698  < 2e-16 ***
regionBaltimoreWashington -2.698e-02  1.909e-02  -1.413 0.157614    
regionBoise               -2.129e-01  1.909e-02 -11.151  < 2e-16 ***
regionBoston              -3.019e-02  1.909e-02  -1.582 0.113769    
regionBuffaloRochester    -4.424e-02  1.909e-02  -2.318 0.020485 *  
regionCalifornia          -1.713e-01  1.919e-02  -8.925  < 2e-16 ***
regionCharlotte            4.497e-02  1.909e-02   2.356 0.018493 *  
regionChicago             -4.616e-03  1.909e-02  -0.242 0.808941    
regionCincinnatiDayton    -3.521e-01  1.909e-02 -18.442  < 2e-16 ***
regionColumbus            -3.084e-01  1.909e-02 -16.157  < 2e-16 ***
regionDallasFtWorth       -4.759e-01  1.909e-02 -24.926  < 2e-16 ***
regionDenver              -3.425e-01  1.909e-02 -17.940  < 2e-16 ***
regionDetroit             -2.866e-01  1.910e-02 -15.008  < 2e-16 ***
regionGrandRapids         -5.688e-02  1.909e-02  -2.979 0.002894 ** 
regionGreatLakes          -2.292e-01  1.923e-02 -11.918  < 2e-16 ***
regionHarrisburgScranton  -4.787e-02  1.909e-02  -2.508 0.012166 *  
regionHartfordSpringfield  2.576e-01  1.909e-02  13.492  < 2e-16 ***
regionHouston             -5.134e-01  1.909e-02 -26.894  < 2e-16 ***
regionIndianapolis        -2.473e-01  1.909e-02 -12.954  < 2e-16 ***
regionJacksonville        -5.015e-02  1.909e-02  -2.627 0.008615 ** 
regionLasVegas            -1.801e-01  1.909e-02  -9.434  < 2e-16 ***
regionLosAngeles          -3.493e-01  1.915e-02 -18.243  < 2e-16 ***
regionLouisville          -2.744e-01  1.909e-02 -14.375  < 2e-16 ***
regionMiamiFtLauderdale   -1.328e-01  1.909e-02  -6.958 3.58e-12 ***
regionMidsouth            -1.577e-01  1.910e-02  -8.257  < 2e-16 ***
regionNashville           -3.490e-01  1.909e-02 -18.282  < 2e-16 ***
regionNewOrleansMobile    -2.567e-01  1.909e-02 -13.448  < 2e-16 ***
regionNewYork              1.662e-01  1.909e-02   8.706  < 2e-16 ***
regionNortheast            3.955e-02  1.910e-02   2.071 0.038381 *  
regionNorthernNewEngland  -8.371e-02  1.909e-02  -4.385 1.17e-05 ***
regionOrlando             -5.503e-02  1.909e-02  -2.883 0.003945 ** 
regionPhiladelphia         7.103e-02  1.909e-02   3.721 0.000199 ***
regionPhoenixTucson       -3.367e-01  1.909e-02 -17.638  < 2e-16 ***
regionPittsburgh          -1.967e-01  1.909e-02 -10.305  < 2e-16 ***
regionPlains              -1.257e-01  1.909e-02  -6.581 4.80e-11 ***
regionPortland            -2.434e-01  1.909e-02 -12.748  < 2e-16 ***
regionRaleighGreensboro   -5.972e-03  1.909e-02  -0.313 0.754415    
regionRichmondNorfolk     -2.698e-01  1.909e-02 -14.132  < 2e-16 ***
regionRoanoke             -3.131e-01  1.909e-02 -16.404  < 2e-16 ***
regionSacramento           6.036e-02  1.909e-02   3.162 0.001571 ** 
regionSanDiego            -1.630e-01  1.909e-02  -8.537  < 2e-16 ***
regionSanFrancisco         2.430e-01  1.909e-02  12.728  < 2e-16 ***
regionSeattle             -1.185e-01  1.909e-02  -6.207 5.52e-10 ***
regionSouthCarolina       -1.579e-01  1.909e-02  -8.274  < 2e-16 ***
regionSouthCentral        -4.625e-01  1.911e-02 -24.199  < 2e-16 ***
regionSoutheast           -1.656e-01  1.911e-02  -8.667  < 2e-16 ***
regionSpokane             -1.154e-01  1.909e-02  -6.045 1.52e-09 ***
regionStLouis             -1.306e-01  1.909e-02  -6.842 8.08e-12 ***
regionSyracuse            -4.071e-02  1.909e-02  -2.132 0.032984 *  
regionTampa               -1.524e-01  1.909e-02  -7.983 1.52e-15 ***
regionTotalUS             -2.647e-01  2.066e-02 -12.815  < 2e-16 ***
regionWest                -2.897e-01  1.909e-02 -15.171  < 2e-16 ***
regionWestTexNewMexico    -2.969e-01  1.913e-02 -15.518  < 2e-16 ***
quarter2                   8.058e-02  5.412e-03  14.891  < 2e-16 ***
quarter3                   2.181e-01  5.414e-03  40.293  < 2e-16 ***
quarter4                   1.621e-01  5.375e-03  30.154  < 2e-16 ***
year2016                  -3.791e-02  4.695e-03  -8.075 7.16e-16 ***
year2017                   1.375e-01  4.680e-03  29.381  < 2e-16 ***
year2018                   8.547e-02  8.360e-03  10.223  < 2e-16 ***
x_large_bags               3.583e-07  1.246e-07   2.877 0.004025 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2482 on 18187 degrees of freedom
Multiple R-squared:  0.6214,    Adjusted R-squared:  0.6202 
F-statistic: 489.4 on 61 and 18187 DF,  p-value: < 2.2e-16

It is a significant explanatory variable, so let’s keep it. Overall, we still have some heterscedasticity and deviations from normality in the residuals.

Let’s now think about possible pair interactions: for five main effect variables we have ten possible pair interactions. Let’s test them out.

model5pa <- lm(average_price ~ type + region + quarter + year + x_large_bags + type:region, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pa)

summary(model5pa)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + type:region, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.00812 -0.13347 -0.00249  0.13359  1.48016 

Coefficients:
                                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)                            1.203e+00  1.855e-02  64.874  < 2e-16 ***
typeorganic                            4.246e-01  2.558e-02  16.598  < 2e-16 ***
regionAtlanta                         -2.801e-01  2.558e-02 -10.950  < 2e-16 ***
regionBaltimoreWashington             -4.684e-03  2.558e-02  -0.183 0.854724    
regionBoise                           -2.727e-01  2.558e-02 -10.660  < 2e-16 ***
regionBoston                          -4.441e-02  2.558e-02  -1.736 0.082557 .  
regionBuffaloRochester                 3.352e-02  2.558e-02   1.310 0.190080    
regionCalifornia                      -2.474e-01  2.600e-02  -9.516  < 2e-16 ***
regionCharlotte                       -7.369e-02  2.558e-02  -2.881 0.003973 ** 
regionChicago                          2.033e-02  2.558e-02   0.795 0.426797    
regionCincinnatiDayton                -3.334e-01  2.558e-02 -13.034  < 2e-16 ***
regionColumbus                        -2.826e-01  2.558e-02 -11.048  < 2e-16 ***
regionDallasFtWorth                   -5.026e-01  2.558e-02 -19.647  < 2e-16 ***
regionDenver                          -2.748e-01  2.558e-02 -10.743  < 2e-16 ***
regionDetroit                         -2.260e-01  2.562e-02  -8.823  < 2e-16 ***
regionGrandRapids                     -2.435e-02  2.559e-02  -0.951 0.341382    
regionGreatLakes                      -1.718e-01  2.619e-02  -6.560 5.54e-11 ***
regionHarrisburgScranton              -9.003e-02  2.558e-02  -3.519 0.000434 ***
regionHartfordSpringfield              5.926e-02  2.558e-02   2.317 0.020528 *  
regionHouston                         -5.239e-01  2.558e-02 -20.479  < 2e-16 ***
regionIndianapolis                    -2.041e-01  2.558e-02  -7.978 1.57e-15 ***
regionJacksonville                    -1.552e-01  2.558e-02  -6.067 1.33e-09 ***
regionLasVegas                        -3.358e-01  2.558e-02 -13.126  < 2e-16 ***
regionLosAngeles                      -3.755e-01  2.583e-02 -14.536  < 2e-16 ***
regionLouisville                      -2.435e-01  2.558e-02  -9.518  < 2e-16 ***
regionMiamiFtLauderdale               -9.464e-02  2.558e-02  -3.700 0.000217 ***
regionMidsouth                        -1.426e-01  2.561e-02  -5.570 2.58e-08 ***
regionNashville                       -3.359e-01  2.558e-02 -13.132  < 2e-16 ***
regionNewOrleansMobile                -2.639e-01  2.558e-02 -10.313  < 2e-16 ***
regionNewYork                          5.313e-02  2.558e-02   2.077 0.037842 *  
regionNortheast                       -5.307e-03  2.560e-02  -0.207 0.835817    
regionNorthernNewEngland              -8.857e-02  2.558e-02  -3.463 0.000536 ***
regionOrlando                         -1.345e-01  2.558e-02  -5.257 1.48e-07 ***
regionPhiladelphia                     4.753e-02  2.558e-02   1.858 0.063204 .  
regionPhoenixTucson                   -6.206e-01  2.558e-02 -24.261  < 2e-16 ***
regionPittsburgh                      -9.812e-02  2.558e-02  -3.836 0.000126 ***
regionPlains                          -1.841e-01  2.560e-02  -7.192 6.66e-13 ***
regionPortland                        -3.023e-01  2.558e-02 -11.817  < 2e-16 ***
regionRaleighGreensboro               -1.217e-01  2.558e-02  -4.757 1.98e-06 ***
regionRichmondNorfolk                 -2.290e-01  2.558e-02  -8.952  < 2e-16 ***
regionRoanoke                         -2.528e-01  2.558e-02  -9.881  < 2e-16 ***
regionSacramento                      -7.492e-02  2.558e-02  -2.929 0.003407 ** 
regionSanDiego                        -2.874e-01  2.558e-02 -11.233  < 2e-16 ***
regionSanFrancisco                     4.827e-02  2.558e-02   1.887 0.059175 .  
regionSeattle                         -1.790e-01  2.558e-02  -6.998 2.69e-12 ***
regionSouthCarolina                   -2.027e-01  2.558e-02  -7.923 2.44e-15 ***
regionSouthCentral                    -4.814e-01  2.568e-02 -18.742  < 2e-16 ***
regionSoutheast                       -1.877e-01  2.567e-02  -7.310 2.79e-13 ***
regionSpokane                         -2.328e-01  2.558e-02  -9.099  < 2e-16 ***
regionStLouis                         -1.632e-01  2.558e-02  -6.378 1.84e-10 ***
regionSyracuse                         3.817e-02  2.558e-02   1.492 0.135705    
regionTampa                           -1.473e-01  2.558e-02  -5.759 8.62e-09 ***
regionTotalUS                         -2.734e-01  3.186e-02  -8.583  < 2e-16 ***
regionWest                            -3.643e-01  2.559e-02 -14.235  < 2e-16 ***
regionWestTexNewMexico                -5.068e-01  2.558e-02 -19.813  < 2e-16 ***
quarter2                               8.101e-02  5.129e-03  15.793  < 2e-16 ***
quarter3                               2.186e-01  5.134e-03  42.587  < 2e-16 ***
quarter4                               1.620e-01  5.093e-03  31.820  < 2e-16 ***
year2016                              -3.735e-02  4.455e-03  -8.385  < 2e-16 ***
year2017                               1.383e-01  4.444e-03  31.110  < 2e-16 ***
year2018                               8.670e-02  7.937e-03  10.923  < 2e-16 ***
x_large_bags                           1.318e-07  1.499e-07   0.879 0.379416    
typeorganic:regionAtlanta              1.139e-01  3.618e-02   3.149 0.001642 ** 
typeorganic:regionBaltimoreWashington -4.437e-02  3.618e-02  -1.226 0.220035    
typeorganic:regionBoise                1.196e-01  3.618e-02   3.307 0.000946 ***
typeorganic:regionBoston               2.849e-02  3.618e-02   0.788 0.430916    
typeorganic:regionBuffaloRochester    -1.555e-01  3.618e-02  -4.298 1.74e-05 ***
typeorganic:regionCalifornia           1.593e-01  3.647e-02   4.367 1.27e-05 ***
typeorganic:regionCharlotte            2.374e-01  3.618e-02   6.561 5.48e-11 ***
typeorganic:regionChicago             -4.944e-02  3.618e-02  -1.367 0.171744    
typeorganic:regionCincinnatiDayton    -3.699e-02  3.618e-02  -1.022 0.306593    
typeorganic:regionColumbus            -5.140e-02  3.618e-02  -1.421 0.155386    
typeorganic:regionDallasFtWorth        5.403e-02  3.618e-02   1.493 0.135327    
typeorganic:regionDenver              -1.353e-01  3.618e-02  -3.741 0.000184 ***
typeorganic:regionDetroit             -1.190e-01  3.620e-02  -3.288 0.001010 ** 
typeorganic:regionGrandRapids         -6.400e-02  3.618e-02  -1.769 0.076968 .  
typeorganic:regionGreatLakes          -1.063e-01  3.661e-02  -2.903 0.003698 ** 
typeorganic:regionHarrisburgScranton   8.447e-02  3.618e-02   2.335 0.019563 *  
typeorganic:regionHartfordSpringfield  3.967e-01  3.618e-02  10.965  < 2e-16 ***
typeorganic:regionHouston              2.134e-02  3.618e-02   0.590 0.555192    
typeorganic:regionIndianapolis        -8.609e-02  3.618e-02  -2.380 0.017343 *  
typeorganic:regionJacksonville         2.102e-01  3.618e-02   5.810 6.37e-09 ***
typeorganic:regionLasVegas             3.113e-01  3.618e-02   8.606  < 2e-16 ***
typeorganic:regionLosAngeles           5.770e-02  3.635e-02   1.587 0.112476    
typeorganic:regionLouisville          -6.178e-02  3.618e-02  -1.708 0.087678 .  
typeorganic:regionMiamiFtLauderdale   -7.601e-02  3.618e-02  -2.101 0.035652 *  
typeorganic:regionMidsouth            -2.831e-02  3.620e-02  -0.782 0.434169    
typeorganic:regionNashville           -2.610e-02  3.618e-02  -0.721 0.470616    
typeorganic:regionNewOrleansMobile     1.486e-02  3.618e-02   0.411 0.681207    
typeorganic:regionNewYork              2.266e-01  3.618e-02   6.263 3.86e-10 ***
typeorganic:regionNortheast            9.140e-02  3.619e-02   2.525 0.011567 *  
typeorganic:regionNorthernNewEngland   9.816e-03  3.618e-02   0.271 0.786139    
typeorganic:regionOrlando              1.591e-01  3.618e-02   4.399 1.09e-05 ***
typeorganic:regionPhiladelphia         4.709e-02  3.618e-02   1.302 0.193037    
typeorganic:regionPhoenixTucson        5.680e-01  3.618e-02  15.700  < 2e-16 ***
typeorganic:regionPittsburgh          -1.972e-01  3.618e-02  -5.451 5.06e-08 ***
typeorganic:regionPlains               1.183e-01  3.619e-02   3.269 0.001082 ** 
typeorganic:regionPortland             1.179e-01  3.618e-02   3.259 0.001120 ** 
typeorganic:regionRaleighGreensboro    2.315e-01  3.618e-02   6.400 1.59e-10 ***
typeorganic:regionRichmondNorfolk     -8.148e-02  3.618e-02  -2.252 0.024322 *  
typeorganic:regionRoanoke             -1.207e-01  3.618e-02  -3.338 0.000847 ***
typeorganic:regionSacramento           2.708e-01  3.618e-02   7.485 7.48e-14 ***
typeorganic:regionSanDiego             2.489e-01  3.618e-02   6.880 6.18e-12 ***
typeorganic:regionSanFrancisco         3.897e-01  3.618e-02  10.771  < 2e-16 ***
typeorganic:regionSeattle              1.211e-01  3.618e-02   3.347 0.000819 ***
typeorganic:regionSouthCarolina        8.973e-02  3.618e-02   2.480 0.013136 *  
typeorganic:regionSouthCentral         4.114e-02  3.625e-02   1.135 0.256458    
typeorganic:regionSoutheast            4.737e-02  3.624e-02   1.307 0.191198    
typeorganic:regionSpokane              2.346e-01  3.618e-02   6.486 9.03e-11 ***
typeorganic:regionStLouis              6.535e-02  3.618e-02   1.806 0.070875 .  
typeorganic:regionSyracuse            -1.578e-01  3.618e-02  -4.361 1.30e-05 ***
typeorganic:regionTampa               -9.910e-03  3.618e-02  -0.274 0.784145    
typeorganic:regionTotalUS              4.616e-02  4.086e-02   1.130 0.258597    
typeorganic:regionWest                 1.503e-01  3.618e-02   4.154 3.28e-05 ***
typeorganic:regionWestTexNewMexico     4.234e-01  3.626e-02  11.676  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2351 on 18134 degrees of freedom
Multiple R-squared:  0.6611,    Adjusted R-squared:  0.659 
F-statistic: 310.3 on 114 and 18134 DF,  p-value: < 2.2e-16
model5pb <- lm(average_price ~ type + region + quarter + year + x_large_bags + type:quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pb)

summary(model5pb)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + type:quarter, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.02270 -0.14602 -0.00362  0.14398  1.44165 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.180e+00  1.454e-02  81.176  < 2e-16 ***
typeorganic                4.717e-01  6.719e-03  70.203  < 2e-16 ***
regionAtlanta             -2.233e-01  1.907e-02 -11.713  < 2e-16 ***
regionBaltimoreWashington -2.699e-02  1.907e-02  -1.416 0.156893    
regionBoise               -2.129e-01  1.907e-02 -11.163  < 2e-16 ***
regionBoston              -3.020e-02  1.907e-02  -1.584 0.113308    
regionBuffaloRochester    -4.425e-02  1.907e-02  -2.320 0.020331 *  
regionCalifornia          -1.718e-01  1.917e-02  -8.962  < 2e-16 ***
regionCharlotte            4.497e-02  1.907e-02   2.358 0.018367 *  
regionChicago             -4.649e-03  1.907e-02  -0.244 0.807387    
regionCincinnatiDayton    -3.521e-01  1.907e-02 -18.465  < 2e-16 ***
regionColumbus            -3.085e-01  1.907e-02 -16.177  < 2e-16 ***
regionDallasFtWorth       -4.759e-01  1.907e-02 -24.957  < 2e-16 ***
regionDenver              -3.425e-01  1.907e-02 -17.960  < 2e-16 ***
regionDetroit             -2.868e-01  1.908e-02 -15.034  < 2e-16 ***
regionGrandRapids         -5.696e-02  1.907e-02  -2.987 0.002824 ** 
regionGreatLakes          -2.298e-01  1.921e-02 -11.964  < 2e-16 ***
regionHarrisburgScranton  -4.788e-02  1.907e-02  -2.511 0.012048 *  
regionHartfordSpringfield  2.576e-01  1.907e-02  13.508  < 2e-16 ***
regionHouston             -5.134e-01  1.907e-02 -26.926  < 2e-16 ***
regionIndianapolis        -2.473e-01  1.907e-02 -12.970  < 2e-16 ***
regionJacksonville        -5.016e-02  1.907e-02  -2.631 0.008531 ** 
regionLasVegas            -1.801e-01  1.907e-02  -9.444  < 2e-16 ***
regionLosAngeles          -3.497e-01  1.913e-02 -18.284  < 2e-16 ***
regionLouisville          -2.744e-01  1.907e-02 -14.392  < 2e-16 ***
regionMiamiFtLauderdale   -1.328e-01  1.907e-02  -6.967 3.35e-12 ***
regionMidsouth            -1.578e-01  1.907e-02  -8.274  < 2e-16 ***
regionNashville           -3.490e-01  1.907e-02 -18.303  < 2e-16 ***
regionNewOrleansMobile    -2.568e-01  1.907e-02 -13.466  < 2e-16 ***
regionNewYork              1.662e-01  1.907e-02   8.714  < 2e-16 ***
regionNortheast            3.942e-02  1.907e-02   2.067 0.038772 *  
regionNorthernNewEngland  -8.372e-02  1.907e-02  -4.390 1.14e-05 ***
regionOrlando             -5.505e-02  1.907e-02  -2.887 0.003892 ** 
regionPhiladelphia         7.102e-02  1.907e-02   3.725 0.000196 ***
regionPhoenixTucson       -3.367e-01  1.907e-02 -17.659  < 2e-16 ***
regionPittsburgh          -1.967e-01  1.907e-02 -10.317  < 2e-16 ***
regionPlains              -1.258e-01  1.907e-02  -6.594 4.39e-11 ***
regionPortland            -2.434e-01  1.907e-02 -12.762  < 2e-16 ***
regionRaleighGreensboro   -5.977e-03  1.907e-02  -0.313 0.753941    
regionRichmondNorfolk     -2.698e-01  1.907e-02 -14.149  < 2e-16 ***
regionRoanoke             -3.131e-01  1.907e-02 -16.423  < 2e-16 ***
regionSacramento           6.034e-02  1.907e-02   3.164 0.001556 ** 
regionSanDiego            -1.630e-01  1.907e-02  -8.548  < 2e-16 ***
regionSanFrancisco         2.430e-01  1.907e-02  12.742  < 2e-16 ***
regionSeattle             -1.185e-01  1.907e-02  -6.214 5.28e-10 ***
regionSouthCarolina       -1.580e-01  1.907e-02  -8.284  < 2e-16 ***
regionSouthCentral        -4.628e-01  1.909e-02 -24.240  < 2e-16 ***
regionSoutheast           -1.659e-01  1.909e-02  -8.690  < 2e-16 ***
regionSpokane             -1.154e-01  1.907e-02  -6.052 1.46e-09 ***
regionStLouis             -1.306e-01  1.907e-02  -6.850 7.60e-12 ***
regionSyracuse            -4.071e-02  1.907e-02  -2.135 0.032785 *  
regionTampa               -1.524e-01  1.907e-02  -7.993 1.40e-15 ***
regionTotalUS             -2.668e-01  2.064e-02 -12.928  < 2e-16 ***
regionWest                -2.897e-01  1.907e-02 -15.193  < 2e-16 ***
regionWestTexNewMexico    -2.969e-01  1.911e-02 -15.537  < 2e-16 ***
quarter2                   6.536e-02  7.416e-03   8.814  < 2e-16 ***
quarter3                   1.848e-01  7.423e-03  24.898  < 2e-16 ***
quarter4                   1.530e-01  7.364e-03  20.776  < 2e-16 ***
year2016                  -3.800e-02  4.689e-03  -8.102 5.72e-16 ***
year2017                   1.374e-01  4.674e-03  29.392  < 2e-16 ***
year2018                   8.529e-02  8.351e-03  10.213  < 2e-16 ***
x_large_bags               3.916e-07  1.246e-07   3.142 0.001682 ** 
typeorganic:quarter2       3.034e-02  1.015e-02   2.989 0.002800 ** 
typeorganic:quarter3       6.653e-02  1.015e-02   6.553 5.80e-11 ***
typeorganic:quarter4       1.817e-02  1.008e-02   1.803 0.071446 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2479 on 18184 degrees of freedom
Multiple R-squared:  0.6224,    Adjusted R-squared:  0.621 
F-statistic: 468.3 on 64 and 18184 DF,  p-value: < 2.2e-16
model5pc <- lm(average_price ~ type + region + quarter + year + x_large_bags + type:year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pc)

summary(model5pc)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + type:year, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.00898 -0.14443 -0.00472  0.13873  1.46680 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.118e+00  1.442e-02  77.501  < 2e-16 ***
typeorganic                5.956e-01  6.569e-03  90.667  < 2e-16 ***
regionAtlanta             -2.232e-01  1.892e-02 -11.796  < 2e-16 ***
regionBaltimoreWashington -2.687e-02  1.892e-02  -1.420 0.155567    
regionBoise               -2.129e-01  1.892e-02 -11.252  < 2e-16 ***
regionBoston              -3.016e-02  1.892e-02  -1.594 0.110873    
regionBuffaloRochester    -4.422e-02  1.892e-02  -2.337 0.019445 *  
regionCalifornia          -1.678e-01  1.902e-02  -8.823  < 2e-16 ***
regionCharlotte            4.499e-02  1.892e-02   2.378 0.017419 *  
regionChicago             -4.393e-03  1.892e-02  -0.232 0.816388    
regionCincinnatiDayton    -3.519e-01  1.892e-02 -18.601  < 2e-16 ***
regionColumbus            -3.083e-01  1.892e-02 -16.297  < 2e-16 ***
regionDallasFtWorth       -4.756e-01  1.892e-02 -25.137  < 2e-16 ***
regionDenver              -3.425e-01  1.892e-02 -18.101  < 2e-16 ***
regionDetroit             -2.856e-01  1.893e-02 -15.087  < 2e-16 ***
regionGrandRapids         -5.635e-02  1.892e-02  -2.978 0.002904 ** 
regionGreatLakes          -2.250e-01  1.906e-02 -11.803  < 2e-16 ***
regionHarrisburgScranton  -4.780e-02  1.892e-02  -2.526 0.011537 *  
regionHartfordSpringfield  2.576e-01  1.892e-02  13.615  < 2e-16 ***
regionHouston             -5.132e-01  1.892e-02 -27.126  < 2e-16 ***
regionIndianapolis        -2.471e-01  1.892e-02 -13.062  < 2e-16 ***
regionJacksonville        -5.011e-02  1.892e-02  -2.649 0.008085 ** 
regionLasVegas            -1.801e-01  1.892e-02  -9.520  < 2e-16 ***
regionLosAngeles          -3.466e-01  1.898e-02 -18.265  < 2e-16 ***
regionLouisville          -2.744e-01  1.892e-02 -14.502  < 2e-16 ***
regionMiamiFtLauderdale   -1.326e-01  1.892e-02  -7.011 2.45e-12 ***
regionMidsouth            -1.568e-01  1.893e-02  -8.285  < 2e-16 ***
regionNashville           -3.490e-01  1.892e-02 -18.445  < 2e-16 ***
regionNewOrleansMobile    -2.564e-01  1.892e-02 -13.553  < 2e-16 ***
regionNewYork              1.664e-01  1.892e-02   8.796  < 2e-16 ***
regionNortheast            4.039e-02  1.893e-02   2.134 0.032855 *  
regionNorthernNewEngland  -8.367e-02  1.892e-02  -4.422 9.83e-06 ***
regionOrlando             -5.490e-02  1.892e-02  -2.902 0.003714 ** 
regionPhiladelphia         7.107e-02  1.892e-02   3.756 0.000173 ***
regionPhoenixTucson       -3.366e-01  1.892e-02 -17.793  < 2e-16 ***
regionPittsburgh          -1.967e-01  1.892e-02 -10.398  < 2e-16 ***
regionPlains              -1.249e-01  1.892e-02  -6.603 4.14e-11 ***
regionPortland            -2.433e-01  1.892e-02 -12.861  < 2e-16 ***
regionRaleighGreensboro   -5.938e-03  1.892e-02  -0.314 0.753649    
regionRichmondNorfolk     -2.697e-01  1.892e-02 -14.257  < 2e-16 ***
regionRoanoke             -3.131e-01  1.892e-02 -16.550  < 2e-16 ***
regionSacramento           6.047e-02  1.892e-02   3.196 0.001396 ** 
regionSanDiego            -1.629e-01  1.892e-02  -8.611  < 2e-16 ***
regionSanFrancisco         2.431e-01  1.892e-02  12.849  < 2e-16 ***
regionSeattle             -1.185e-01  1.892e-02  -6.262 3.89e-10 ***
regionSouthCarolina       -1.578e-01  1.892e-02  -8.342  < 2e-16 ***
regionSouthCentral        -4.608e-01  1.894e-02 -24.326  < 2e-16 ***
regionSoutheast           -1.640e-01  1.894e-02  -8.658  < 2e-16 ***
regionSpokane             -1.154e-01  1.892e-02  -6.101 1.07e-09 ***
regionStLouis             -1.305e-01  1.892e-02  -6.897 5.49e-12 ***
regionSyracuse            -4.071e-02  1.892e-02  -2.152 0.031432 *  
regionTampa               -1.523e-01  1.892e-02  -8.048 8.93e-16 ***
regionTotalUS             -2.505e-01  2.049e-02 -12.226  < 2e-16 ***
regionWest                -2.891e-01  1.892e-02 -15.280  < 2e-16 ***
regionWestTexNewMexico    -2.967e-01  1.896e-02 -15.650  < 2e-16 ***
quarter2                   8.091e-02  5.363e-03  15.085  < 2e-16 ***
quarter3                   2.186e-01  5.366e-03  40.744  < 2e-16 ***
quarter4                   1.620e-01  5.327e-03  30.417  < 2e-16 ***
year2016                   2.694e-02  6.596e-03   4.084 4.45e-05 ***
year2017                   2.152e-01  6.582e-03  32.691  < 2e-16 ***
year2018                   1.641e-01  1.128e-02  14.549  < 2e-16 ***
x_large_bags               1.338e-07  1.241e-07   1.078 0.281087    
typeorganic:year2016      -1.285e-01  9.306e-03 -13.813  < 2e-16 ***
typeorganic:year2017      -1.540e-01  9.275e-03 -16.600  < 2e-16 ***
typeorganic:year2018      -1.548e-01  1.520e-02 -10.184  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.246 on 18184 degrees of freedom
Multiple R-squared:  0.6282,    Adjusted R-squared:  0.6269 
F-statistic: 480.1 on 64 and 18184 DF,  p-value: < 2.2e-16
model5pd <- lm(average_price ~ type + region + quarter + year + x_large_bags + type:x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pd)

summary(model5pd)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + type:x_large_bags, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.03574 -0.14591 -0.00478  0.14434  1.43935 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.168e+00  1.429e-02  81.734  < 2e-16 ***
typeorganic                4.978e-01  3.757e-03 132.483  < 2e-16 ***
regionAtlanta             -2.233e-01  1.909e-02 -11.701  < 2e-16 ***
regionBaltimoreWashington -2.699e-02  1.909e-02  -1.414 0.157339    
regionBoise               -2.130e-01  1.909e-02 -11.159  < 2e-16 ***
regionBoston              -3.020e-02  1.909e-02  -1.582 0.113671    
regionBuffaloRochester    -4.425e-02  1.909e-02  -2.318 0.020456 *  
regionCalifornia          -1.717e-01  1.918e-02  -8.949  < 2e-16 ***
regionCharlotte            4.497e-02  1.909e-02   2.356 0.018481 *  
regionChicago             -4.644e-03  1.909e-02  -0.243 0.807777    
regionCincinnatiDayton    -3.521e-01  1.909e-02 -18.446  < 2e-16 ***
regionColumbus            -3.085e-01  1.909e-02 -16.160  < 2e-16 ***
regionDallasFtWorth       -4.759e-01  1.909e-02 -24.932  < 2e-16 ***
regionDenver              -3.425e-01  1.909e-02 -17.943  < 2e-16 ***
regionDetroit             -2.868e-01  1.910e-02 -15.017  < 2e-16 ***
regionGrandRapids         -5.695e-02  1.909e-02  -2.983 0.002857 ** 
regionGreatLakes          -2.297e-01  1.923e-02 -11.947  < 2e-16 ***
regionHarrisburgScranton  -4.788e-02  1.909e-02  -2.508 0.012135 *  
regionHartfordSpringfield  2.576e-01  1.909e-02  13.494  < 2e-16 ***
regionHouston             -5.134e-01  1.909e-02 -26.899  < 2e-16 ***
regionIndianapolis        -2.473e-01  1.909e-02 -12.957  < 2e-16 ***
regionJacksonville        -5.016e-02  1.909e-02  -2.628 0.008598 ** 
regionLasVegas            -1.801e-01  1.909e-02  -9.435  < 2e-16 ***
regionLosAngeles          -3.496e-01  1.915e-02 -18.263  < 2e-16 ***
regionLouisville          -2.744e-01  1.909e-02 -14.377  < 2e-16 ***
regionMiamiFtLauderdale   -1.328e-01  1.909e-02  -6.960 3.52e-12 ***
regionMidsouth            -1.578e-01  1.909e-02  -8.265  < 2e-16 ***
regionNashville           -3.490e-01  1.909e-02 -18.285  < 2e-16 ***
regionNewOrleansMobile    -2.568e-01  1.909e-02 -13.453  < 2e-16 ***
regionNewYork              1.662e-01  1.909e-02   8.706  < 2e-16 ***
regionNortheast            3.944e-02  1.909e-02   2.066 0.038871 *  
regionNorthernNewEngland  -8.372e-02  1.909e-02  -4.386 1.16e-05 ***
regionOrlando             -5.505e-02  1.909e-02  -2.884 0.003929 ** 
regionPhiladelphia         7.102e-02  1.909e-02   3.721 0.000199 ***
regionPhoenixTucson       -3.367e-01  1.909e-02 -17.642  < 2e-16 ***
regionPittsburgh          -1.967e-01  1.909e-02 -10.307  < 2e-16 ***
regionPlains              -1.258e-01  1.909e-02  -6.589 4.56e-11 ***
regionPortland            -2.447e-01  1.909e-02 -12.817  < 2e-16 ***
regionRaleighGreensboro   -5.976e-03  1.909e-02  -0.313 0.754207    
regionRichmondNorfolk     -2.698e-01  1.909e-02 -14.135  < 2e-16 ***
regionRoanoke             -3.131e-01  1.909e-02 -16.406  < 2e-16 ***
regionSacramento           6.034e-02  1.909e-02   3.161 0.001572 ** 
regionSanDiego            -1.630e-01  1.909e-02  -8.539  < 2e-16 ***
regionSanFrancisco         2.430e-01  1.909e-02  12.730  < 2e-16 ***
regionSeattle             -1.212e-01  1.912e-02  -6.341 2.34e-10 ***
regionSouthCarolina       -1.580e-01  1.909e-02  -8.276  < 2e-16 ***
regionSouthCentral        -4.628e-01  1.911e-02 -24.214  < 2e-16 ***
regionSoutheast           -1.658e-01  1.911e-02  -8.679  < 2e-16 ***
regionSpokane             -1.156e-01  1.909e-02  -6.056 1.42e-09 ***
regionStLouis             -1.306e-01  1.909e-02  -6.843 7.98e-12 ***
regionSyracuse            -4.071e-02  1.909e-02  -2.133 0.032957 *  
regionTampa               -1.524e-01  1.909e-02  -7.985 1.49e-15 ***
regionTotalUS             -2.719e-01  2.084e-02 -13.048  < 2e-16 ***
regionWest                -2.951e-01  1.920e-02 -15.366  < 2e-16 ***
regionWestTexNewMexico    -2.970e-01  1.913e-02 -15.524  < 2e-16 ***
quarter2                   8.054e-02  5.411e-03  14.885  < 2e-16 ***
quarter3                   2.180e-01  5.414e-03  40.259  < 2e-16 ***
quarter4                   1.616e-01  5.377e-03  30.058  < 2e-16 ***
year2016                  -3.798e-02  4.694e-03  -8.092 6.25e-16 ***
year2017                   1.370e-01  4.684e-03  29.241  < 2e-16 ***
year2018                   8.319e-02  8.405e-03   9.898  < 2e-16 ***
x_large_bags               3.865e-07  1.250e-07   3.091 0.001995 ** 
typeorganic:x_large_bags   4.737e-04  1.827e-04   2.593 0.009522 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2481 on 18186 degrees of freedom
Multiple R-squared:  0.6216,    Adjusted R-squared:  0.6203 
F-statistic: 481.8 on 62 and 18186 DF,  p-value: < 2.2e-16
model5pe <- lm(average_price ~ type + region + quarter + year + x_large_bags + region:quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pe)

summary(model5pe)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + region:quarter, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.06468 -0.14582  0.00048  0.14087  1.38018 

Coefficients:
                                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         1.216e+00  2.423e-02  50.190  < 2e-16 ***
typeorganic                         4.985e-01  3.663e-03 136.095  < 2e-16 ***
regionAtlanta                      -2.579e-01  3.388e-02  -7.611 2.85e-14 ***
regionBaltimoreWashington          -8.986e-02  3.388e-02  -2.652 0.008000 ** 
regionBoise                        -2.854e-01  3.388e-02  -8.424  < 2e-16 ***
regionBoston                       -7.093e-03  3.388e-02  -0.209 0.834158    
regionBuffaloRochester             -3.109e-02  3.388e-02  -0.918 0.358774    
regionCalifornia                   -2.868e-01  3.394e-02  -8.450  < 2e-16 ***
regionCharlotte                    -2.147e-02  3.388e-02  -0.634 0.526347    
regionChicago                      -7.400e-02  3.388e-02  -2.184 0.028945 *  
regionCincinnatiDayton             -4.353e-01  3.388e-02 -12.849  < 2e-16 ***
regionColumbus                     -3.251e-01  3.388e-02  -9.595  < 2e-16 ***
regionDallasFtWorth                -4.853e-01  3.388e-02 -14.325  < 2e-16 ***
regionDenver                       -4.216e-01  3.388e-02 -12.443  < 2e-16 ***
regionDetroit                      -3.074e-01  3.389e-02  -9.071  < 2e-16 ***
regionGrandRapids                  -1.295e-01  3.388e-02  -3.824 0.000132 ***
regionGreatLakes                   -2.769e-01  3.398e-02  -8.150 3.88e-16 ***
regionHarrisburgScranton           -6.005e-02  3.388e-02  -1.773 0.076319 .  
regionHartfordSpringfield           2.290e-01  3.388e-02   6.759 1.43e-11 ***
regionHouston                      -5.375e-01  3.388e-02 -15.867  < 2e-16 ***
regionIndianapolis                 -2.742e-01  3.388e-02  -8.093 6.20e-16 ***
regionJacksonville                 -1.104e-01  3.388e-02  -3.259 0.001121 ** 
regionLasVegas                     -2.907e-01  3.388e-02  -8.581  < 2e-16 ***
regionLosAngeles                   -4.383e-01  3.391e-02 -12.923  < 2e-16 ***
regionLouisville                   -2.956e-01  3.388e-02  -8.725  < 2e-16 ***
regionMiamiFtLauderdale            -1.119e-01  3.388e-02  -3.302 0.000962 ***
regionMidsouth                     -1.953e-01  3.388e-02  -5.764 8.33e-09 ***
regionNashville                    -3.514e-01  3.388e-02 -10.372  < 2e-16 ***
regionNewOrleansMobile             -3.177e-01  3.388e-02  -9.377  < 2e-16 ***
regionNewYork                       1.048e-01  3.388e-02   3.094 0.001979 ** 
regionNortheast                     1.933e-02  3.388e-02   0.570 0.568361    
regionNorthernNewEngland           -5.982e-02  3.388e-02  -1.766 0.077455 .  
regionOrlando                      -1.034e-01  3.388e-02  -3.053 0.002269 ** 
regionPhiladelphia                  1.650e-02  3.388e-02   0.487 0.626253    
regionPhoenixTucson                -4.456e-01  3.388e-02 -13.153  < 2e-16 ***
regionPittsburgh                   -1.745e-01  3.388e-02  -5.151 2.62e-07 ***
regionPlains                       -1.852e-01  3.388e-02  -5.466 4.67e-08 ***
regionPortland                     -3.533e-01  3.388e-02 -10.429  < 2e-16 ***
regionRaleighGreensboro            -5.803e-02  3.388e-02  -1.713 0.086751 .  
regionRichmondNorfolk              -2.636e-01  3.388e-02  -7.782 7.52e-15 ***
regionRoanoke                      -3.123e-01  3.388e-02  -9.217  < 2e-16 ***
regionSacramento                   -2.741e-02  3.388e-02  -0.809 0.418472    
regionSanDiego                     -2.868e-01  3.388e-02  -8.466  < 2e-16 ***
regionSanFrancisco                  9.026e-02  3.388e-02   2.664 0.007726 ** 
regionSeattle                      -2.589e-01  3.388e-02  -7.642 2.25e-14 ***
regionSouthCarolina                -2.071e-01  3.388e-02  -6.114 9.93e-10 ***
regionSouthCentral                 -4.798e-01  3.390e-02 -14.153  < 2e-16 ***
regionSoutheast                    -2.084e-01  3.388e-02  -6.151 7.88e-10 ***
regionSpokane                      -2.696e-01  3.388e-02  -7.958 1.85e-15 ***
regionStLouis                      -1.910e-01  3.388e-02  -5.639 1.74e-08 ***
regionSyracuse                     -2.764e-02  3.388e-02  -0.816 0.414661    
regionTampa                        -1.532e-01  3.388e-02  -4.523 6.14e-06 ***
regionTotalUS                      -3.151e-01  3.466e-02  -9.091  < 2e-16 ***
regionWest                         -3.903e-01  3.388e-02 -11.520  < 2e-16 ***
regionWestTexNewMexico             -3.665e-01  3.388e-02 -10.818  < 2e-16 ***
quarter2                            8.528e-02  3.644e-02   2.341 0.019266 *  
quarter3                            9.278e-02  3.644e-02   2.546 0.010895 *  
quarter4                            7.165e-02  3.618e-02   1.981 0.047660 *  
year2016                           -3.808e-02  4.577e-03  -8.319  < 2e-16 ***
year2017                            1.373e-01  4.563e-03  30.081  < 2e-16 ***
year2018                            8.513e-02  8.151e-03  10.444  < 2e-16 ***
x_large_bags                        4.158e-07  1.233e-07   3.373 0.000746 ***
regionAtlanta:quarter2             -8.875e-02  5.147e-02  -1.725 0.084627 .  
regionBaltimoreWashington:quarter2  9.216e-02  5.147e-02   1.791 0.073359 .  
regionBoise:quarter2               -9.544e-02  5.147e-02  -1.854 0.063692 .  
regionBoston:quarter2               1.139e-02  5.147e-02   0.221 0.824911    
regionBuffaloRochester:quarter2     8.166e-02  5.147e-02   1.587 0.112579    
regionCalifornia:quarter2           4.240e-03  5.147e-02   0.082 0.934345    
regionCharlotte:quarter2            6.218e-02  5.147e-02   1.208 0.226952    
regionChicago:quarter2             -4.249e-03  5.147e-02  -0.083 0.934198    
regionCincinnatiDayton:quarter2     1.014e-02  5.147e-02   0.197 0.843877    
regionColumbus:quarter2            -9.402e-02  5.147e-02  -1.827 0.067727 .  
regionDallasFtWorth:quarter2       -7.789e-02  5.147e-02  -1.513 0.130177    
regionDenver:quarter2              -1.578e-02  5.147e-02  -0.307 0.759141    
regionDetroit:quarter2             -3.691e-02  5.147e-02  -0.717 0.473257    
regionGrandRapids:quarter2          1.363e-01  5.147e-02   2.649 0.008086 ** 
regionGreatLakes:quarter2          -1.091e-02  5.147e-02  -0.212 0.832191    
regionHarrisburgScranton:quarter2   6.543e-02  5.147e-02   1.271 0.203625    
regionHartfordSpringfield:quarter2  6.725e-02  5.147e-02   1.307 0.191332    
regionHouston:quarter2             -8.920e-02  5.147e-02  -1.733 0.083088 .  
regionIndianapolis:quarter2        -6.425e-02  5.147e-02  -1.248 0.211928    
regionJacksonville:quarter2         2.811e-02  5.147e-02   0.546 0.584928    
regionLasVegas:quarter2            -7.424e-02  5.147e-02  -1.443 0.149173    
regionLosAngeles:quarter2          -6.060e-02  5.147e-02  -1.177 0.239049    
regionLouisville:quarter2          -7.449e-02  5.147e-02  -1.447 0.147834    
regionMiamiFtLauderdale:quarter2   -1.020e-02  5.147e-02  -0.198 0.842828    
regionMidsouth:quarter2            -1.515e-02  5.147e-02  -0.294 0.768501    
regionNashville:quarter2           -1.026e-01  5.147e-02  -1.993 0.046304 *  
regionNewOrleansMobile:quarter2     8.341e-02  5.147e-02   1.621 0.105105    
regionNewYork:quarter2              8.732e-02  5.147e-02   1.697 0.089772 .  
regionNortheast:quarter2            5.500e-02  5.147e-02   1.069 0.285265    
regionNorthernNewEngland:quarter2  -6.770e-02  5.147e-02  -1.316 0.188354    
regionOrlando:quarter2              1.769e-02  5.147e-02   0.344 0.731089    
regionPhiladelphia:quarter2         1.100e-01  5.147e-02   2.137 0.032587 *  
regionPhoenixTucson:quarter2       -1.980e-02  5.147e-02  -0.385 0.700459    
regionPittsburgh:quarter2          -3.807e-02  5.147e-02  -0.740 0.459513    
regionPlains:quarter2              -4.009e-03  5.147e-02  -0.078 0.937911    
regionPortland:quarter2            -4.527e-02  5.147e-02  -0.880 0.379084    
regionRaleighGreensboro:quarter2    1.832e-03  5.147e-02   0.036 0.971604    
regionRichmondNorfolk:quarter2     -1.137e-01  5.147e-02  -2.209 0.027195 *  
regionRoanoke:quarter2             -1.312e-01  5.147e-02  -2.550 0.010779 *  
regionSacramento:quarter2           8.446e-02  5.147e-02   1.641 0.100786    
regionSanDiego:quarter2            -3.285e-03  5.147e-02  -0.064 0.949106    
regionSanFrancisco:quarter2         1.221e-01  5.147e-02   2.373 0.017637 *  
regionSeattle:quarter2              1.210e-02  5.147e-02   0.235 0.814101    
regionSouthCarolina:quarter2        2.735e-02  5.147e-02   0.531 0.595172    
regionSouthCentral:quarter2        -7.164e-02  5.147e-02  -1.392 0.163922    
regionSoutheast:quarter2           -9.837e-03  5.148e-02  -0.191 0.848456    
regionSpokane:quarter2              9.803e-03  5.147e-02   0.190 0.848939    
regionStLouis:quarter2              5.672e-02  5.147e-02   1.102 0.270444    
regionSyracuse:quarter2             6.494e-02  5.147e-02   1.262 0.207015    
regionTampa:quarter2                5.706e-03  5.147e-02   0.111 0.911722    
regionTotalUS:quarter2             -1.476e-02  5.149e-02  -0.287 0.774329    
regionWest:quarter2                -2.856e-02  5.147e-02  -0.555 0.578953    
regionWestTexNewMexico:quarter2    -9.603e-02  5.166e-02  -1.859 0.063053 .  
regionAtlanta:quarter3              1.224e-01  5.147e-02   2.378 0.017422 *  
regionBaltimoreWashington:quarter3  9.538e-02  5.147e-02   1.853 0.063854 .  
regionBoise:quarter3                2.521e-01  5.147e-02   4.898 9.79e-07 ***
regionBoston:quarter3              -1.212e-03  5.147e-02  -0.024 0.981214    
regionBuffaloRochester:quarter3    -3.416e-02  5.147e-02  -0.664 0.506909    
regionCalifornia:quarter3           2.572e-01  5.147e-02   4.996 5.89e-07 ***
regionCharlotte:quarter3            1.397e-01  5.147e-02   2.715 0.006641 ** 
regionChicago:quarter3              1.740e-01  5.147e-02   3.381 0.000723 ***
regionCincinnatiDayton:quarter3     2.128e-01  5.147e-02   4.135 3.57e-05 ***
regionColumbus:quarter3             1.094e-01  5.147e-02   2.126 0.033525 *  
regionDallasFtWorth:quarter3        2.363e-02  5.147e-02   0.459 0.646184    
regionDenver:quarter3               2.124e-01  5.147e-02   4.128 3.68e-05 ***
regionDetroit:quarter3              5.517e-02  5.147e-02   1.072 0.283742    
regionGrandRapids:quarter3          9.166e-02  5.147e-02   1.781 0.074936 .  
regionGreatLakes:quarter3           1.228e-01  5.147e-02   2.387 0.017003 *  
regionHarrisburgScranton:quarter3   6.457e-03  5.147e-02   0.125 0.900153    
regionHartfordSpringfield:quarter3  4.942e-02  5.147e-02   0.960 0.336930    
regionHouston:quarter3              7.247e-02  5.147e-02   1.408 0.159093    
regionIndianapolis:quarter3         9.223e-02  5.147e-02   1.792 0.073138 .  
regionJacksonville:quarter3         1.680e-01  5.147e-02   3.265 0.001098 ** 
regionLasVegas:quarter3             2.954e-01  5.147e-02   5.740 9.61e-09 ***
regionLosAngeles:quarter3           2.150e-01  5.147e-02   4.178 2.96e-05 ***
regionLouisville:quarter3           8.478e-02  5.147e-02   1.647 0.099505 .  
regionMiamiFtLauderdale:quarter3   -7.307e-02  5.147e-02  -1.420 0.155672    
regionMidsouth:quarter3             9.249e-02  5.147e-02   1.797 0.072360 .  
regionNashville:quarter3            4.167e-02  5.147e-02   0.810 0.418085    
regionNewOrleansMobile:quarter3     7.109e-02  5.147e-02   1.381 0.167222    
regionNewYork:quarter3              1.121e-01  5.147e-02   2.177 0.029476 *  
regionNortheast:quarter3            4.725e-02  5.147e-02   0.918 0.358649    
regionNorthernNewEngland:quarter3  -1.389e-02  5.147e-02  -0.270 0.787273    
regionOrlando:quarter3              1.156e-01  5.147e-02   2.245 0.024762 *  
regionPhiladelphia:quarter3         8.202e-02  5.147e-02   1.594 0.111012    
regionPhoenixTucson:quarter3        2.603e-01  5.147e-02   5.058 4.27e-07 ***
regionPittsburgh:quarter3          -1.622e-02  5.147e-02  -0.315 0.752619    
regionPlains:quarter3               1.348e-01  5.147e-02   2.619 0.008837 ** 
regionPortland:quarter3             3.344e-01  5.147e-02   6.498 8.33e-11 ***
regionRaleighGreensboro:quarter3    1.211e-01  5.147e-02   2.354 0.018600 *  
regionRichmondNorfolk:quarter3      5.134e-02  5.147e-02   0.998 0.318528    
regionRoanoke:quarter3              9.037e-02  5.147e-02   1.756 0.079127 .  
regionSacramento:quarter3           1.815e-01  5.147e-02   3.527 0.000421 ***
regionSanDiego:quarter3             2.805e-01  5.147e-02   5.451 5.08e-08 ***
regionSanFrancisco:quarter3         3.126e-01  5.147e-02   6.074 1.27e-09 ***
regionSeattle:quarter3              3.922e-01  5.147e-02   7.620 2.66e-14 ***
regionSouthCarolina:quarter3        1.023e-01  5.147e-02   1.987 0.046905 *  
regionSouthCentral:quarter3         4.390e-02  5.147e-02   0.853 0.393732    
regionSoutheast:quarter3            1.067e-01  5.148e-02   2.073 0.038179 *  
regionSpokane:quarter3              3.937e-01  5.147e-02   7.650 2.11e-14 ***
regionStLouis:quarter3              1.916e-01  5.147e-02   3.723 0.000197 ***
regionSyracuse:quarter3            -3.686e-02  5.147e-02  -0.716 0.473930    
regionTampa:quarter3               -4.372e-02  5.147e-02  -0.850 0.395566    
regionTotalUS:quarter3              9.405e-02  5.156e-02   1.824 0.068183 .  
regionWest:quarter3                 2.980e-01  5.147e-02   5.791 7.13e-09 ***
regionWestTexNewMexico:quarter3     1.785e-01  5.147e-02   3.469 0.000523 ***
regionAtlanta:quarter4              1.130e-01  5.110e-02   2.210 0.027086 *  
regionBaltimoreWashington:quarter4  8.270e-02  5.110e-02   1.618 0.105581    
regionBoise:quarter4                1.538e-01  5.110e-02   3.009 0.002626 ** 
regionBoston:quarter4              -1.075e-01  5.110e-02  -2.105 0.035345 *  
regionBuffaloRochester:quarter4    -1.019e-01  5.110e-02  -1.994 0.046129 *  
regionCalifornia:quarter4           2.298e-01  5.110e-02   4.496 6.96e-06 ***
regionCharlotte:quarter4            8.383e-02  5.110e-02   1.641 0.100897    
regionChicago:quarter4              1.274e-01  5.110e-02   2.493 0.012665 *  
regionCincinnatiDayton:quarter4     1.341e-01  5.110e-02   2.625 0.008682 ** 
regionColumbus:quarter4             5.517e-02  5.110e-02   1.080 0.280283    
regionDallasFtWorth:quarter4        9.257e-02  5.110e-02   1.811 0.070085 .  
regionDenver:quarter4               1.424e-01  5.110e-02   2.787 0.005319 ** 
regionDetroit:quarter4              6.867e-02  5.110e-02   1.344 0.179058    
regionGrandRapids:quarter4          8.416e-02  5.110e-02   1.647 0.099577 .  
regionGreatLakes:quarter4           8.786e-02  5.111e-02   1.719 0.085637 .  
regionHarrisburgScranton:quarter4  -1.870e-02  5.110e-02  -0.366 0.714421    
regionHartfordSpringfield:quarter4  7.018e-03  5.110e-02   0.137 0.890763    
regionHouston:quarter4              1.181e-01  5.110e-02   2.311 0.020852 *  
regionIndianapolis:quarter4         8.610e-02  5.110e-02   1.685 0.092029 .  
regionJacksonville:quarter4         6.326e-02  5.110e-02   1.238 0.215724    
regionLasVegas:quarter4             2.517e-01  5.110e-02   4.925 8.50e-07 ***
regionLosAngeles:quarter4           2.225e-01  5.110e-02   4.354 1.34e-05 ***
regionLouisville:quarter4           7.942e-02  5.110e-02   1.554 0.120131    
regionMiamiFtLauderdale:quarter4   -7.519e-03  5.110e-02  -0.147 0.883012    
regionMidsouth:quarter4             8.252e-02  5.110e-02   1.615 0.106367    
regionNashville:quarter4            6.942e-02  5.110e-02   1.358 0.174327    
regionNewOrleansMobile:quarter4     1.065e-01  5.110e-02   2.085 0.037083 *  
regionNewYork:quarter4              6.475e-02  5.110e-02   1.267 0.205122    
regionNortheast:quarter4           -1.518e-02  5.110e-02  -0.297 0.766432    
regionNorthernNewEngland:quarter4  -2.143e-02  5.110e-02  -0.419 0.674965    
regionOrlando:quarter4              7.442e-02  5.110e-02   1.456 0.145298    
regionPhiladelphia:quarter4         4.312e-02  5.110e-02   0.844 0.398758    
 [ reached getOption("max.print") -- omitted 21 rows ]
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2419 on 18028 degrees of freedom
Multiple R-squared:  0.6434,    Adjusted R-squared:  0.639 
F-statistic: 147.8 on 220 and 18028 DF,  p-value: < 2.2e-16

model5pf <- lm(average_price ~ type + region + quarter + year + x_large_bags + region:year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pf)

summary(model5pf)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + region:year, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.03187 -0.14124 -0.00167  0.13786  1.38842 

Coefficients:
                                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         1.175e+00  2.396e-02  49.024  < 2e-16 ***
typeorganic                         4.975e-01  3.662e-03 135.876  < 2e-16 ***
regionAtlanta                      -1.582e-01  3.348e-02  -4.724 2.33e-06 ***
regionBaltimoreWashington          -1.699e-01  3.348e-02  -5.075 3.92e-07 ***
regionBoise                        -1.650e-01  3.348e-02  -4.928 8.38e-07 ***
regionBoston                       -6.519e-02  3.348e-02  -1.947 0.051546 .  
regionBuffaloRochester              5.865e-03  3.348e-02   0.175 0.860943    
regionCalifornia                   -2.234e-01  3.348e-02  -6.671 2.61e-11 ***
regionCharlotte                     3.702e-02  3.348e-02   1.106 0.268906    
regionChicago                      -1.348e-01  3.348e-02  -4.026 5.69e-05 ***
regionCincinnatiDayton             -3.367e-01  3.348e-02 -10.056  < 2e-16 ***
regionColumbus                     -2.651e-01  3.348e-02  -7.919 2.54e-15 ***
regionDallasFtWorth                -4.610e-01  3.348e-02 -13.768  < 2e-16 ***
regionDenver                       -3.510e-01  3.348e-02 -10.482  < 2e-16 ***
regionDetroit                      -2.016e-01  3.349e-02  -6.021 1.77e-09 ***
regionGrandRapids                  -1.226e-01  3.348e-02  -3.662 0.000251 ***
regionGreatLakes                   -2.160e-01  3.353e-02  -6.442 1.21e-10 ***
regionHarrisburgScranton           -6.714e-02  3.348e-02  -2.005 0.044969 *  
regionHartfordSpringfield           2.090e-01  3.348e-02   6.243 4.38e-10 ***
regionHouston                      -4.908e-01  3.348e-02 -14.659  < 2e-16 ***
regionIndianapolis                 -1.960e-01  3.348e-02  -5.854 4.87e-09 ***
regionJacksonville                 -3.567e-02  3.348e-02  -1.065 0.286701    
regionLasVegas                     -1.699e-01  3.348e-02  -5.074 3.93e-07 ***
regionLosAngeles                   -3.867e-01  3.348e-02 -11.549  < 2e-16 ***
regionLouisville                   -2.444e-01  3.348e-02  -7.300 3.00e-13 ***
regionMiamiFtLauderdale            -1.552e-01  3.348e-02  -4.635 3.59e-06 ***
regionMidsouth                     -1.876e-01  3.348e-02  -5.603 2.13e-08 ***
regionNashville                    -2.616e-01  3.348e-02  -7.812 5.95e-15 ***
regionNewOrleansMobile             -2.711e-01  3.348e-02  -8.095 6.07e-16 ***
regionNewYork                       1.058e-01  3.348e-02   3.159 0.001587 ** 
regionNortheast                     4.958e-03  3.348e-02   0.148 0.882293    
regionNorthernNewEngland           -6.538e-02  3.348e-02  -1.953 0.050862 .  
regionOrlando                      -3.943e-02  3.348e-02  -1.177 0.239023    
regionPhiladelphia                  1.644e-02  3.348e-02   0.491 0.623441    
regionPhoenixTucson                -3.816e-01  3.348e-02 -11.398  < 2e-16 ***
regionPittsburgh                   -1.315e-01  3.348e-02  -3.929 8.58e-05 ***
regionPlains                       -1.011e-01  3.348e-02  -3.019 0.002543 ** 
regionPortland                     -2.320e-01  3.348e-02  -6.928 4.41e-12 ***
regionRaleighGreensboro            -8.933e-02  3.348e-02  -2.668 0.007641 ** 
regionRichmondNorfolk              -2.642e-01  3.348e-02  -7.892 3.15e-15 ***
regionRoanoke                      -3.116e-01  3.348e-02  -9.307  < 2e-16 ***
regionSacramento                   -8.471e-02  3.348e-02  -2.530 0.011414 *  
regionSanDiego                     -2.645e-01  3.348e-02  -7.900 2.94e-15 ***
regionSanFrancisco                  8.230e-02  3.348e-02   2.458 0.013980 *  
regionSeattle                      -1.166e-01  3.348e-02  -3.481 0.000501 ***
regionSouthCarolina                -8.404e-02  3.348e-02  -2.510 0.012085 *  
regionSouthCentral                 -4.272e-01  3.348e-02 -12.759  < 2e-16 ***
regionSoutheast                    -1.241e-01  3.348e-02  -3.705 0.000212 ***
regionSpokane                      -1.384e-01  3.348e-02  -4.132 3.61e-05 ***
regionStLouis                      -3.539e-02  3.348e-02  -1.057 0.290606    
regionSyracuse                     -9.711e-03  3.348e-02  -0.290 0.771793    
regionTampa                        -1.821e-01  3.348e-02  -5.439 5.42e-08 ***
regionTotalUS                      -2.864e-01  3.358e-02  -8.531  < 2e-16 ***
regionWest                         -3.011e-01  3.348e-02  -8.992  < 2e-16 ***
regionWestTexNewMexico             -2.767e-01  3.356e-02  -8.243  < 2e-16 ***
quarter2                            8.069e-02  5.265e-03  15.325  < 2e-16 ***
quarter3                            2.184e-01  5.268e-03  41.450  < 2e-16 ***
quarter4                            1.620e-01  5.229e-03  30.989  < 2e-16 ***
year2016                           -4.861e-03  3.348e-02  -0.145 0.884570    
year2017                            9.815e-02  3.332e-02   2.945 0.003230 ** 
year2018                            1.233e-02  5.477e-02   0.225 0.821920    
x_large_bags                        2.575e-07  1.277e-07   2.017 0.043674 *  
regionAtlanta:year2016             -1.617e-01  4.735e-02  -3.414 0.000641 ***
regionBaltimoreWashington:year2016  2.234e-01  4.735e-02   4.718 2.40e-06 ***
regionBoise:year2016               -2.270e-01  4.735e-02  -4.793 1.65e-06 ***
regionBoston:year2016              -4.263e-02  4.735e-02  -0.900 0.367957    
regionBuffaloRochester:year2016    -5.600e-02  4.735e-02  -1.183 0.237011    
regionCalifornia:year2016           1.603e-02  4.737e-02   0.338 0.735153    
regionCharlotte:year2016           -7.308e-02  4.735e-02  -1.543 0.122784    
regionChicago:year2016              1.479e-01  4.735e-02   3.123 0.001794 ** 
regionCincinnatiDayton:year2016    -1.091e-01  4.735e-02  -2.304 0.021212 *  
regionColumbus:year2016            -8.266e-02  4.735e-02  -1.746 0.080880 .  
regionDallasFtWorth:year2016       -7.729e-02  4.735e-02  -1.632 0.102631    
regionDenver:year2016              -8.983e-02  4.735e-02  -1.897 0.057824 .  
regionDetroit:year2016             -1.613e-01  4.735e-02  -3.406 0.000661 ***
regionGrandRapids:year2016          9.775e-02  4.735e-02   2.064 0.038991 *  
regionGreatLakes:year2016          -4.595e-02  4.736e-02  -0.970 0.331929    
regionHarrisburgScranton:year2016   4.470e-02  4.735e-02   0.944 0.345203    
regionHartfordSpringfield:year2016  1.080e-01  4.735e-02   2.282 0.022511 *  
regionHouston:year2016             -5.176e-02  4.735e-02  -1.093 0.274356    
regionIndianapolis:year2016        -3.665e-02  4.735e-02  -0.774 0.438916    
regionJacksonville:year2016        -1.307e-01  4.735e-02  -2.759 0.005797 ** 
regionLasVegas:year2016            -1.159e-02  4.735e-02  -0.245 0.806598    
regionLosAngeles:year2016          -6.631e-02  4.737e-02  -1.400 0.161523    
regionLouisville:year2016          -7.807e-02  4.735e-02  -1.649 0.099214 .  
regionMiamiFtLauderdale:year2016   -9.933e-02  4.735e-02  -2.098 0.035939 *  
regionMidsouth:year2016             3.128e-03  4.736e-02   0.066 0.947330    
regionNashville:year2016           -1.562e-01  4.735e-02  -3.299 0.000971 ***
regionNewOrleansMobile:year2016    -1.471e-02  4.735e-02  -0.311 0.756016    
regionNewYork:year2016              1.222e-01  4.735e-02   2.581 0.009869 ** 
regionNortheast:year2016            5.556e-02  4.736e-02   1.173 0.240727    
regionNorthernNewEngland:year2016  -7.595e-02  4.735e-02  -1.604 0.108755    
regionOrlando:year2016             -1.241e-01  4.735e-02  -2.620 0.008803 ** 
regionPhiladelphia:year2016         1.244e-01  4.735e-02   2.627 0.008634 ** 
regionPhoenixTucson:year2016        1.065e-01  4.735e-02   2.248 0.024571 *  
regionPittsburgh:year2016          -5.907e-02  4.735e-02  -1.247 0.212245    
regionPlains:year2016              -5.670e-02  4.736e-02  -1.197 0.231193    
regionPortland:year2016            -1.103e-01  4.735e-02  -2.330 0.019806 *  
regionRaleighGreensboro:year2016    3.099e-03  4.735e-02   0.065 0.947823    
regionRichmondNorfolk:year2016     -5.864e-02  4.735e-02  -1.238 0.215586    
regionRoanoke:year2016             -7.486e-02  4.735e-02  -1.581 0.113932    
regionSacramento:year2016           2.189e-01  4.735e-02   4.623 3.80e-06 ***
regionSanDiego:year2016             4.432e-02  4.735e-02   0.936 0.349308    
regionSanFrancisco:year2016         2.650e-01  4.735e-02   5.596 2.23e-08 ***
regionSeattle:year2016             -1.171e-01  4.735e-02  -2.473 0.013403 *  
regionSouthCarolina:year2016       -1.449e-01  4.735e-02  -3.060 0.002215 ** 
regionSouthCentral:year2016        -8.303e-02  4.737e-02  -1.753 0.079655 .  
regionSoutheast:year2016           -1.250e-01  4.736e-02  -2.640 0.008305 ** 
regionSpokane:year2016             -6.197e-02  4.735e-02  -1.309 0.190631    
regionStLouis:year2016             -3.134e-01  4.735e-02  -6.619 3.73e-11 ***
regionSyracuse:year2016            -2.077e-02  4.735e-02  -0.439 0.660952    
regionTampa:year2016               -8.761e-02  4.735e-02  -1.850 0.064290 .  
regionTotalUS:year2016             -2.523e-03  4.782e-02  -0.053 0.957917    
regionWest:year2016                -5.260e-02  4.735e-02  -1.111 0.266681    
regionWestTexNewMexico:year2016    -1.118e-02  4.741e-02  -0.236 0.813538    
regionAtlanta:year2017             -5.133e-02  4.713e-02  -1.089 0.276065    
regionBaltimoreWashington:year2017  2.113e-01  4.713e-02   4.483 7.40e-06 ***
regionBoise:year2017                1.985e-02  4.713e-02   0.421 0.673552    
regionBoston:year2017               1.068e-01  4.713e-02   2.267 0.023398 *  
regionBuffaloRochester:year2017    -5.601e-02  4.713e-02  -1.189 0.234633    
regionCalifornia:year2017           1.126e-01  4.723e-02   2.384 0.017123 *  
regionCharlotte:year2017            9.489e-02  4.713e-02   2.013 0.044081 *  
regionChicago:year2017              2.114e-01  4.713e-02   4.486 7.31e-06 ***
regionCincinnatiDayton:year2017     1.831e-02  4.713e-02   0.389 0.697600    
regionColumbus:year2017            -5.701e-02  4.713e-02  -1.210 0.226414    
regionDallasFtWorth:year2017        1.122e-04  4.713e-02   0.002 0.998100    
regionDenver:year2017               7.089e-02  4.713e-02   1.504 0.132563    
regionDetroit:year2017             -9.823e-02  4.713e-02  -2.084 0.037149 *  
regionGrandRapids:year2017          1.115e-01  4.713e-02   2.366 0.017969 *  
regionGreatLakes:year2017          -2.282e-03  4.713e-02  -0.048 0.961394    
regionHarrisburgScranton:year2017   2.497e-02  4.713e-02   0.530 0.596285    
regionHartfordSpringfield:year2017  4.139e-02  4.713e-02   0.878 0.379792    
regionHouston:year2017             -4.291e-02  4.713e-02  -0.911 0.362553    
regionIndianapolis:year2017        -1.111e-01  4.713e-02  -2.357 0.018445 *  
regionJacksonville:year2017         6.928e-02  4.713e-02   1.470 0.141549    
regionLasVegas:year2017            -5.007e-02  4.713e-02  -1.062 0.288096    
regionLosAngeles:year2017           1.211e-01  4.719e-02   2.566 0.010299 *  
regionLouisville:year2017          -3.632e-02  4.713e-02  -0.771 0.440950    
regionMiamiFtLauderdale:year2017    1.547e-01  4.713e-02   3.282 0.001034 ** 
regionMidsouth:year2017             6.894e-02  4.713e-02   1.463 0.143549    
regionNashville:year2017           -1.364e-01  4.713e-02  -2.894 0.003810 ** 
regionNewOrleansMobile:year2017     5.163e-02  4.713e-02   1.095 0.273319    
regionNewYork:year2017              6.570e-02  4.713e-02   1.394 0.163320    
regionNortheast:year2017            4.965e-02  4.713e-02   1.053 0.292145    
regionNorthernNewEngland:year2017   4.649e-03  4.713e-02   0.099 0.921414    
regionOrlando:year2017              8.160e-02  4.713e-02   1.731 0.083380 .  
regionPhiladelphia:year2017         5.293e-02  4.713e-02   1.123 0.261438    
regionPhoenixTucson:year2017        1.622e-02  4.713e-02   0.344 0.730705    
regionPittsburgh:year2017          -1.434e-01  4.713e-02  -3.042 0.002352 ** 
regionPlains:year2017              -2.733e-02  4.713e-02  -0.580 0.561981    
regionPortland:year2017             2.846e-02  4.713e-02   0.604 0.545918    
regionRaleighGreensboro:year2017    2.201e-01  4.713e-02   4.671 3.02e-06 ***
regionRichmondNorfolk:year2017      2.554e-02  4.713e-02   0.542 0.587832    
regionRoanoke:year2017              3.208e-02  4.713e-02   0.681 0.496074    
regionSacramento:year2017           2.207e-01  4.713e-02   4.683 2.84e-06 ***
regionSanDiego:year2017             2.111e-01  4.713e-02   4.478 7.57e-06 ***
regionSanFrancisco:year2017         2.455e-01  4.713e-02   5.210 1.91e-07 ***
regionSeattle:year2017              7.804e-02  4.713e-02   1.656 0.097776 .  
regionSouthCarolina:year2017       -7.433e-02  4.713e-02  -1.577 0.114754    
regionSouthCentral:year2017        -4.930e-02  4.713e-02  -1.046 0.295573    
regionSoutheast:year2017           -5.160e-03  4.716e-02  -0.109 0.912881    
regionSpokane:year2017              1.051e-01  4.713e-02   2.230 0.025752 *  
regionStLouis:year2017             -1.074e-02  4.713e-02  -0.228 0.819670    
regionSyracuse:year2017            -3.869e-02  4.713e-02  -0.821 0.411693    
regionTampa:year2017                1.635e-01  4.713e-02   3.469 0.000525 ***
regionTotalUS:year2017              6.318e-02  4.787e-02   1.320 0.186917    
regionWest:year2017                 5.256e-02  4.713e-02   1.115 0.264729    
regionWestTexNewMexico:year2017    -7.553e-02  4.730e-02  -1.597 0.110308    
regionAtlanta:year2018              1.072e-02  7.733e-02   0.139 0.889782    
regionBaltimoreWashington:year2018  1.124e-01  7.733e-02   1.453 0.146104    
regionBoise:year2018                2.217e-01  7.733e-02   2.867 0.004149 ** 
regionBoston:year2018               2.059e-01  7.733e-02   2.663 0.007742 ** 
regionBuffaloRochester:year2018    -2.155e-01  7.733e-02  -2.787 0.005332 ** 
regionCalifornia:year2018           1.892e-01  7.746e-02   2.443 0.014578 *  
regionCharlotte:year2018            9.679e-03  7.733e-02   0.125 0.900390    
regionChicago:year2018              2.606e-01  7.733e-02   3.370 0.000753 ***
regionCincinnatiDayton:year2018     1.764e-01  7.733e-02   2.281 0.022553 *  
regionColumbus:year2018             9.079e-04  7.733e-02   0.012 0.990632    
regionDallasFtWorth:year2018        1.265e-01  7.733e-02   1.636 0.101773    
regionDenver:year2018               1.960e-01  7.733e-02   2.535 0.011261 *  
regionDetroit:year2018             -5.785e-02  7.733e-02  -0.748 0.454421    
regionGrandRapids:year2018          1.287e-02  7.733e-02   0.166 0.867847    
regionGreatLakes:year2018           4.963e-02  7.737e-02   0.642 0.521201    
regionHarrisburgScranton:year2018  -3.216e-02  7.733e-02  -0.416 0.677506    
regionHartfordSpringfield:year2018  3.256e-02  7.733e-02   0.421 0.673717    
regionHouston:year2018              9.701e-02  7.733e-02   1.255 0.209633    
regionIndianapolis:year2018        -7.169e-02  7.733e-02  -0.927 0.353907    
regionJacksonville:year2018         5.652e-02  7.733e-02   0.731 0.464859    
regionLasVegas:year2018             1.278e-01  7.733e-02   1.653 0.098411 .  
regionLosAngeles:year2018           2.964e-01  7.738e-02   3.831 0.000128 ***
regionLouisville:year2018           7.646e-02  7.733e-02   0.989 0.322751    
regionMiamiFtLauderdale:year2018    6.354e-02  7.733e-02   0.822 0.411224    
regionMidsouth:year2018             1.091e-01  7.733e-02   1.411 0.158407    
regionNashville:year2018            4.803e-02  7.733e-02   0.621 0.534514    
regionNewOrleansMobile:year2018     3.935e-02  7.733e-02   0.509 0.610832    
regionNewYork:year2018              3.283e-02  7.733e-02   0.425 0.671123    
regionNortheast:year2018            3.237e-02  7.733e-02   0.419 0.675477    
regionNorthernNewEngland:year2018   5.076e-02  7.733e-02   0.656 0.511534    
regionOrlando:year2018             -4.181e-02  7.733e-02  -0.541 0.588694    
regionPhiladelphia:year2018        -3.644e-03  7.733e-02  -0.047 0.962413    
 [ reached getOption("max.print") -- omitted 21 rows ]
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2414 on 18028 degrees of freedom
Multiple R-squared:  0.6448,    Adjusted R-squared:  0.6405 
F-statistic: 148.8 on 220 and 18028 DF,  p-value: < 2.2e-16
model5pg <- lm(average_price ~ type + region + quarter + year + x_large_bags + region:x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pg)

summary(model5pg)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + region:x_large_bags, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.00590 -0.14516 -0.00347  0.14267  1.44125 

Coefficients:
                                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)                             1.157e+00  1.475e-02  78.422  < 2e-16 ***
typeorganic                             4.999e-01  4.037e-03 123.829  < 2e-16 ***
regionAtlanta                          -2.087e-01  2.013e-02 -10.371  < 2e-16 ***
regionBaltimoreWashington              -3.231e-02  1.986e-02  -1.627 0.103767    
regionBoise                            -1.940e-01  1.977e-02  -9.809  < 2e-16 ***
regionBoston                           -3.887e-02  1.994e-02  -1.949 0.051298 .  
regionBuffaloRochester                 -3.757e-02  1.981e-02  -1.896 0.057934 .  
regionCalifornia                       -1.486e-01  2.138e-02  -6.952 3.73e-12 ***
regionCharlotte                         5.896e-02  1.972e-02   2.989 0.002799 ** 
regionChicago                          -1.992e-02  2.044e-02  -0.975 0.329738    
regionCincinnatiDayton                 -3.552e-01  2.050e-02 -17.331  < 2e-16 ***
regionColumbus                         -3.118e-01  2.049e-02 -15.216  < 2e-16 ***
regionDallasFtWorth                    -4.683e-01  1.983e-02 -23.612  < 2e-16 ***
regionDenver                           -3.389e-01  1.973e-02 -17.180  < 2e-16 ***
regionDetroit                          -3.106e-01  2.107e-02 -14.743  < 2e-16 ***
regionGrandRapids                      -7.090e-02  2.040e-02  -3.475 0.000512 ***
regionGreatLakes                       -2.471e-01  2.142e-02 -11.533  < 2e-16 ***
regionHarrisburgScranton               -3.937e-02  1.982e-02  -1.986 0.047013 *  
regionHartfordSpringfield               2.737e-01  1.994e-02  13.724  < 2e-16 ***
regionHouston                          -5.100e-01  1.971e-02 -25.876  < 2e-16 ***
regionIndianapolis                     -2.525e-01  2.077e-02 -12.158  < 2e-16 ***
regionJacksonville                     -3.545e-02  1.987e-02  -1.784 0.074463 .  
regionLasVegas                         -1.643e-01  1.982e-02  -8.289  < 2e-16 ***
regionLosAngeles                       -3.536e-01  2.157e-02 -16.388  < 2e-16 ***
regionLouisville                       -2.774e-01  2.048e-02 -13.545  < 2e-16 ***
regionMiamiFtLauderdale                -1.309e-01  1.981e-02  -6.605 4.08e-11 ***
regionMidsouth                         -1.541e-01  2.005e-02  -7.685 1.60e-14 ***
regionNashville                        -3.399e-01  2.060e-02 -16.496  < 2e-16 ***
regionNewOrleansMobile                 -2.666e-01  2.032e-02 -13.122  < 2e-16 ***
regionNewYork                           1.685e-01  1.998e-02   8.431  < 2e-16 ***
regionNortheast                         4.073e-02  1.997e-02   2.039 0.041431 *  
regionNorthernNewEngland               -8.220e-02  1.977e-02  -4.158 3.22e-05 ***
regionOrlando                          -3.994e-02  1.979e-02  -2.019 0.043541 *  
regionPhiladelphia                      7.529e-02  1.985e-02   3.792 0.000150 ***
regionPhoenixTucson                    -2.935e-01  1.998e-02 -14.689  < 2e-16 ***
regionPittsburgh                       -1.966e-01  1.969e-02  -9.988  < 2e-16 ***
regionPlains                           -1.101e-01  2.035e-02  -5.409 6.42e-08 ***
regionPortland                         -2.287e-01  2.014e-02 -11.354  < 2e-16 ***
regionRaleighGreensboro                 8.980e-03  1.965e-02   0.457 0.647707    
regionRichmondNorfolk                  -2.639e-01  1.975e-02 -13.361  < 2e-16 ***
regionRoanoke                          -3.083e-01  1.979e-02 -15.577  < 2e-16 ***
regionSacramento                        9.105e-02  2.024e-02   4.498 6.89e-06 ***
regionSanDiego                         -1.403e-01  2.038e-02  -6.887 5.89e-12 ***
regionSanFrancisco                      2.908e-01  2.051e-02  14.180  < 2e-16 ***
regionSeattle                          -1.056e-01  2.097e-02  -5.035 4.81e-07 ***
regionSouthCarolina                    -1.508e-01  2.000e-02  -7.541 4.87e-14 ***
regionSouthCentral                     -4.547e-01  2.026e-02 -22.448  < 2e-16 ***
regionSoutheast                        -1.581e-01  2.016e-02  -7.843 4.63e-15 ***
regionSpokane                          -8.415e-02  2.025e-02  -4.156 3.25e-05 ***
regionStLouis                          -1.118e-01  1.972e-02  -5.670 1.45e-08 ***
regionSyracuse                         -3.950e-02  1.975e-02  -2.000 0.045480 *  
regionTampa                            -1.470e-01  1.980e-02  -7.427 1.16e-13 ***
regionTotalUS                          -2.436e-01  2.125e-02 -11.463  < 2e-16 ***
regionWest                             -2.673e-01  2.074e-02 -12.891  < 2e-16 ***
regionWestTexNewMexico                 -2.812e-01  1.972e-02 -14.260  < 2e-16 ***
quarter2                                7.926e-02  5.408e-03  14.654  < 2e-16 ***
quarter3                                2.156e-01  5.472e-03  39.402  < 2e-16 ***
quarter4                                1.645e-01  5.346e-03  30.762  < 2e-16 ***
year2016                               -3.867e-02  4.730e-03  -8.175 3.14e-16 ***
year2017                                1.399e-01  4.764e-03  29.355  < 2e-16 ***
year2018                                9.389e-02  8.481e-03  11.071  < 2e-16 ***
x_large_bags                            6.780e-05  3.165e-05   2.142 0.032202 *  
regionAtlanta:x_large_bags             -7.465e-05  3.229e-05  -2.311 0.020817 *  
regionBaltimoreWashington:x_large_bags -4.459e-05  3.238e-05  -1.377 0.168604    
regionBoise:x_large_bags               -3.981e-04  1.293e-04  -3.079 0.002077 ** 
regionBoston:x_large_bags               1.603e-06  3.660e-05   0.044 0.965060    
regionBuffaloRochester:x_large_bags    -5.922e-05  3.576e-05  -1.656 0.097767 .  
regionCalifornia:x_large_bags          -6.834e-05  3.165e-05  -2.159 0.030867 *  
regionCharlotte:x_large_bags           -9.327e-05  3.610e-05  -2.584 0.009779 ** 
regionChicago:x_large_bags             -4.606e-05  3.215e-05  -1.433 0.151906    
regionCincinnatiDayton:x_large_bags    -5.231e-05  3.275e-05  -1.597 0.110224    
regionColumbus:x_large_bags            -4.902e-05  3.321e-05  -1.476 0.139968    
regionDallasFtWorth:x_large_bags       -6.657e-05  3.181e-05  -2.093 0.036381 *  
regionDenver:x_large_bags              -3.469e-05  3.926e-05  -0.884 0.376950    
regionDetroit:x_large_bags             -6.075e-05  3.169e-05  -1.917 0.055232 .  
regionGrandRapids:x_large_bags         -5.830e-05  3.174e-05  -1.837 0.066265 .  
regionGreatLakes:x_large_bags          -6.604e-05  3.165e-05  -2.086 0.036958 *  
regionHarrisburgScranton:x_large_bags  -6.708e-05  3.286e-05  -2.042 0.041194 *  
regionHartfordSpringfield:x_large_bags -9.982e-05  3.752e-05  -2.660 0.007810 ** 
regionHouston:x_large_bags             -6.198e-05  3.185e-05  -1.946 0.051713 .  
regionIndianapolis:x_large_bags        -5.092e-05  3.283e-05  -1.551 0.120934    
regionJacksonville:x_large_bags        -8.681e-05  3.455e-05  -2.513 0.011991 *  
regionLasVegas:x_large_bags            -2.179e-04  9.195e-05  -2.370 0.017784 *  
regionLosAngeles:x_large_bags          -6.637e-05  3.166e-05  -2.097 0.036039 *  
regionLouisville:x_large_bags          -3.106e-05  3.772e-05  -0.823 0.410237    
regionMiamiFtLauderdale:x_large_bags   -6.002e-05  3.195e-05  -1.879 0.060329 .  
regionMidsouth:x_large_bags            -6.620e-05  3.167e-05  -2.090 0.036587 *  
regionNashville:x_large_bags           -6.882e-05  3.798e-05  -1.812 0.070007 .  
regionNewOrleansMobile:x_large_bags    -5.523e-05  3.188e-05  -1.732 0.083257 .  
regionNewYork:x_large_bags             -6.142e-05  3.195e-05  -1.922 0.054590 .  
regionNortheast:x_large_bags           -6.551e-05  3.167e-05  -2.069 0.038594 *  
regionNorthernNewEngland:x_large_bags  -4.558e-05  3.371e-05  -1.352 0.176342    
regionOrlando:x_large_bags             -7.638e-05  3.209e-05  -2.380 0.017329 *  
regionPhiladelphia:x_large_bags        -5.342e-05  3.439e-05  -1.553 0.120351    
regionPhoenixTucson:x_large_bags       -1.429e-04  3.331e-05  -4.291 1.79e-05 ***
regionPittsburgh:x_large_bags          -1.719e-05  3.737e-05  -0.460 0.645586    
regionPlains:x_large_bags              -6.954e-05  3.170e-05  -2.194 0.028244 *  
regionPortland:x_large_bags            -9.347e-05  3.944e-05  -2.370 0.017806 *  
regionRaleighGreensboro:x_large_bags   -8.980e-05  3.359e-05  -2.674 0.007512 ** 
regionRichmondNorfolk:x_large_bags     -5.979e-05  3.324e-05  -1.799 0.072098 .  
regionRoanoke:x_large_bags             -5.109e-05  3.583e-05  -1.426 0.153899    
regionSacramento:x_large_bags          -1.031e-04  3.298e-05  -3.126 0.001774 ** 
regionSanDiego:x_large_bags            -1.000e-04  3.480e-05  -2.874 0.004055 ** 
regionSanFrancisco:x_large_bags        -1.300e-04  3.336e-05  -3.896 9.81e-05 ***
regionSeattle:x_large_bags             -8.839e-05  5.055e-05  -1.749 0.080361 .  
regionSouthCarolina:x_large_bags       -6.511e-05  3.246e-05  -2.006 0.044848 *  
regionSouthCentral:x_large_bags        -6.733e-05  3.166e-05  -2.127 0.033439 *  
regionSoutheast:x_large_bags           -6.729e-05  3.166e-05  -2.126 0.033558 *  
regionSpokane:x_large_bags             -1.130e-03  2.762e-04  -4.093 4.28e-05 ***
regionStLouis:x_large_bags             -8.268e-05  3.208e-05  -2.577 0.009971 ** 
regionSyracuse:x_large_bags            -7.061e-06  4.375e-05  -0.161 0.871772    
regionTampa:x_large_bags               -6.270e-05  3.214e-05  -1.951 0.051068 .  
regionTotalUS:x_large_bags             -6.764e-05  3.165e-05  -2.137 0.032614 *  
regionWest:x_large_bags                -7.298e-05  3.178e-05  -2.297 0.021641 *  
regionWestTexNewMexico:x_large_bags    -7.497e-05  3.184e-05  -2.354 0.018573 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2465 on 18134 degrees of freedom
Multiple R-squared:  0.6276,    Adjusted R-squared:  0.6253 
F-statistic: 268.1 on 114 and 18134 DF,  p-value: < 2.2e-16
model5ph <- lm(average_price ~ type + region + quarter + year + x_large_bags + quarter:year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5ph)

summary(model5ph)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + quarter:year, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.96209 -0.13588 -0.00192  0.13567  1.48311 

Coefficients: (3 not defined because of singularities)
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.259e+00  1.454e-02  86.603  < 2e-16 ***
typeorganic                4.983e-01  3.630e-03 137.274  < 2e-16 ***
regionAtlanta             -2.233e-01  1.846e-02 -12.101  < 2e-16 ***
regionBaltimoreWashington -2.699e-02  1.846e-02  -1.463 0.143613    
regionBoise               -2.129e-01  1.846e-02 -11.533  < 2e-16 ***
regionBoston              -3.020e-02  1.846e-02  -1.636 0.101842    
regionBuffaloRochester    -4.425e-02  1.846e-02  -2.397 0.016525 *  
regionCalifornia          -1.717e-01  1.855e-02  -9.257  < 2e-16 ***
regionCharlotte            4.497e-02  1.846e-02   2.437 0.014836 *  
regionChicago             -4.646e-03  1.846e-02  -0.252 0.801250    
regionCincinnatiDayton    -3.521e-01  1.846e-02 -19.077  < 2e-16 ***
regionColumbus            -3.085e-01  1.846e-02 -16.713  < 2e-16 ***
regionDallasFtWorth       -4.759e-01  1.846e-02 -25.784  < 2e-16 ***
regionDenver              -3.425e-01  1.846e-02 -18.556  < 2e-16 ***
regionDetroit             -2.868e-01  1.847e-02 -15.531  < 2e-16 ***
regionGrandRapids         -5.695e-02  1.846e-02  -3.085 0.002036 ** 
regionGreatLakes          -2.298e-01  1.859e-02 -12.358  < 2e-16 ***
regionHarrisburgScranton  -4.788e-02  1.846e-02  -2.594 0.009488 ** 
regionHartfordSpringfield  2.576e-01  1.846e-02  13.955  < 2e-16 ***
regionHouston             -5.134e-01  1.846e-02 -27.819  < 2e-16 ***
regionIndianapolis        -2.473e-01  1.846e-02 -13.400  < 2e-16 ***
regionJacksonville        -5.016e-02  1.846e-02  -2.718 0.006578 ** 
regionLasVegas            -1.801e-01  1.846e-02  -9.758  < 2e-16 ***
regionLosAngeles          -3.497e-01  1.851e-02 -18.888  < 2e-16 ***
regionLouisville          -2.744e-01  1.846e-02 -14.869  < 2e-16 ***
regionMiamiFtLauderdale   -1.328e-01  1.846e-02  -7.198 6.36e-13 ***
regionMidsouth            -1.578e-01  1.846e-02  -8.548  < 2e-16 ***
regionNashville           -3.490e-01  1.846e-02 -18.910  < 2e-16 ***
regionNewOrleansMobile    -2.568e-01  1.846e-02 -13.913  < 2e-16 ***
regionNewYork              1.662e-01  1.846e-02   9.004  < 2e-16 ***
regionNortheast            3.943e-02  1.846e-02   2.136 0.032703 *  
regionNorthernNewEngland  -8.372e-02  1.846e-02  -4.536 5.77e-06 ***
regionOrlando             -5.505e-02  1.846e-02  -2.983 0.002860 ** 
regionPhiladelphia         7.102e-02  1.846e-02   3.848 0.000119 ***
regionPhoenixTucson       -3.367e-01  1.846e-02 -18.245  < 2e-16 ***
regionPittsburgh          -1.967e-01  1.846e-02 -10.659  < 2e-16 ***
regionPlains              -1.258e-01  1.846e-02  -6.812 9.90e-12 ***
regionPortland            -2.434e-01  1.846e-02 -13.185  < 2e-16 ***
regionRaleighGreensboro   -5.977e-03  1.846e-02  -0.324 0.746076    
regionRichmondNorfolk     -2.698e-01  1.846e-02 -14.618  < 2e-16 ***
regionRoanoke             -3.131e-01  1.846e-02 -16.967  < 2e-16 ***
regionSacramento           6.034e-02  1.846e-02   3.269 0.001079 ** 
regionSanDiego            -1.630e-01  1.846e-02  -8.831  < 2e-16 ***
regionSanFrancisco         2.430e-01  1.846e-02  13.165  < 2e-16 ***
regionSeattle             -1.185e-01  1.846e-02  -6.420 1.40e-10 ***
regionSouthCarolina       -1.580e-01  1.846e-02  -8.559  < 2e-16 ***
regionSouthCentral        -4.628e-01  1.848e-02 -25.043  < 2e-16 ***
regionSoutheast           -1.659e-01  1.848e-02  -8.977  < 2e-16 ***
regionSpokane             -1.154e-01  1.846e-02  -6.253 4.12e-10 ***
regionStLouis             -1.306e-01  1.846e-02  -7.077 1.52e-12 ***
regionSyracuse            -4.071e-02  1.846e-02  -2.206 0.027420 *  
regionTampa               -1.524e-01  1.846e-02  -8.258  < 2e-16 ***
regionTotalUS             -2.666e-01  1.998e-02 -13.348  < 2e-16 ***
regionWest                -2.897e-01  1.846e-02 -15.696  < 2e-16 ***
regionWestTexNewMexico    -2.969e-01  1.850e-02 -16.051  < 2e-16 ***
quarter2                   2.117e-02  9.056e-03   2.338 0.019420 *  
quarter3                   8.279e-02  9.056e-03   9.142  < 2e-16 ***
quarter4                  -1.080e-02  9.058e-03  -1.192 0.233314    
year2016                  -1.186e-01  9.059e-03 -13.097  < 2e-16 ***
year2017                  -5.756e-02  9.061e-03  -6.352 2.17e-10 ***
year2018                  -6.568e-03  9.262e-03  -0.709 0.478278    
x_large_bags               3.887e-07  1.206e-07   3.222 0.001273 ** 
quarter2:year2016         -2.921e-02  1.281e-02  -2.281 0.022572 *  
quarter3:year2016          9.430e-02  1.281e-02   7.362 1.89e-13 ***
quarter4:year2016          2.576e-01  1.281e-02  20.108  < 2e-16 ***
quarter2:year2017          2.074e-01  1.281e-02  16.187  < 2e-16 ***
quarter3:year2017          3.116e-01  1.281e-02  24.323  < 2e-16 ***
quarter4:year2017          2.620e-01  1.270e-02  20.641  < 2e-16 ***
quarter2:year2018                 NA         NA      NA       NA    
quarter3:year2018                 NA         NA      NA       NA    
quarter4:year2018                 NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2399 on 18181 degrees of freedom
Multiple R-squared:  0.6463,    Adjusted R-squared:  0.645 
F-statistic: 495.8 on 67 and 18181 DF,  p-value: < 2.2e-16
model5pi <- lm(average_price ~ type + region + quarter + year + x_large_bags + quarter:x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pi)

summary(model5pi)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + quarter:x_large_bags, data = trimmed_avocados)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.0362 -0.1455 -0.0045  0.1442  1.4394 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.167e+00  1.429e-02  81.659  < 2e-16 ***
typeorganic                4.981e-01  3.765e-03 132.295  < 2e-16 ***
regionAtlanta             -2.233e-01  1.909e-02 -11.698  < 2e-16 ***
regionBaltimoreWashington -2.698e-02  1.909e-02  -1.413 0.157567    
regionBoise               -2.129e-01  1.909e-02 -11.150  < 2e-16 ***
regionBoston              -3.019e-02  1.909e-02  -1.581 0.113792    
regionBuffaloRochester    -4.424e-02  1.909e-02  -2.317 0.020490 *  
regionCalifornia          -1.710e-01  1.923e-02  -8.894  < 2e-16 ***
regionCharlotte            4.497e-02  1.909e-02   2.356 0.018507 *  
regionChicago             -4.605e-03  1.909e-02  -0.241 0.809395    
regionCincinnatiDayton    -3.521e-01  1.909e-02 -18.440  < 2e-16 ***
regionColumbus            -3.084e-01  1.909e-02 -16.156  < 2e-16 ***
regionDallasFtWorth       -4.758e-01  1.909e-02 -24.922  < 2e-16 ***
regionDenver              -3.425e-01  1.909e-02 -17.938  < 2e-16 ***
regionDetroit             -2.866e-01  1.910e-02 -15.004  < 2e-16 ***
regionGrandRapids         -5.683e-02  1.909e-02  -2.977 0.002919 ** 
regionGreatLakes          -2.290e-01  1.926e-02 -11.892  < 2e-16 ***
regionHarrisburgScranton  -4.787e-02  1.909e-02  -2.507 0.012170 *  
regionHartfordSpringfield  2.576e-01  1.909e-02  13.491  < 2e-16 ***
regionHouston             -5.134e-01  1.909e-02 -26.891  < 2e-16 ***
regionIndianapolis        -2.473e-01  1.909e-02 -12.953  < 2e-16 ***
regionJacksonville        -5.016e-02  1.909e-02  -2.627 0.008616 ** 
regionLasVegas            -1.801e-01  1.909e-02  -9.433  < 2e-16 ***
regionLosAngeles          -3.492e-01  1.917e-02 -18.212  < 2e-16 ***
regionLouisville          -2.744e-01  1.909e-02 -14.374  < 2e-16 ***
regionMiamiFtLauderdale   -1.328e-01  1.909e-02  -6.958 3.57e-12 ***
regionMidsouth            -1.577e-01  1.910e-02  -8.258  < 2e-16 ***
regionNashville           -3.490e-01  1.909e-02 -18.281  < 2e-16 ***
regionNewOrleansMobile    -2.567e-01  1.909e-02 -13.447  < 2e-16 ***
regionNewYork              1.662e-01  1.909e-02   8.705  < 2e-16 ***
regionNortheast            3.951e-02  1.910e-02   2.069 0.038564 *  
regionNorthernNewEngland  -8.371e-02  1.909e-02  -4.385 1.17e-05 ***
regionOrlando             -5.505e-02  1.909e-02  -2.883 0.003941 ** 
regionPhiladelphia         7.103e-02  1.909e-02   3.721 0.000199 ***
regionPhoenixTucson       -3.367e-01  1.909e-02 -17.636  < 2e-16 ***
regionPittsburgh          -1.967e-01  1.909e-02 -10.305  < 2e-16 ***
regionPlains              -1.257e-01  1.910e-02  -6.582 4.78e-11 ***
regionPortland            -2.433e-01  1.909e-02 -12.746  < 2e-16 ***
regionRaleighGreensboro   -5.973e-03  1.909e-02  -0.313 0.754386    
regionRichmondNorfolk     -2.698e-01  1.909e-02 -14.132  < 2e-16 ***
regionRoanoke             -3.131e-01  1.909e-02 -16.402  < 2e-16 ***
regionSacramento           6.037e-02  1.909e-02   3.162 0.001568 ** 
regionSanDiego            -1.630e-01  1.909e-02  -8.536  < 2e-16 ***
regionSanFrancisco         2.430e-01  1.909e-02  12.728  < 2e-16 ***
regionSeattle             -1.185e-01  1.909e-02  -6.206 5.55e-10 ***
regionSouthCarolina       -1.580e-01  1.909e-02  -8.273  < 2e-16 ***
regionSouthCentral        -4.624e-01  1.912e-02 -24.183  < 2e-16 ***
regionSoutheast           -1.657e-01  1.911e-02  -8.671  < 2e-16 ***
regionSpokane             -1.154e-01  1.909e-02  -6.045 1.53e-09 ***
regionStLouis             -1.306e-01  1.909e-02  -6.841 8.09e-12 ***
regionSyracuse            -4.071e-02  1.909e-02  -2.132 0.032995 *  
regionTampa               -1.524e-01  1.909e-02  -7.983 1.52e-15 ***
regionTotalUS             -2.643e-01  2.085e-02 -12.677  < 2e-16 ***
regionWest                -2.896e-01  1.910e-02 -15.166  < 2e-16 ***
regionWestTexNewMexico    -2.969e-01  1.913e-02 -15.516  < 2e-16 ***
quarter2                   8.023e-02  5.472e-03  14.661  < 2e-16 ***
quarter3                   2.180e-01  5.470e-03  39.862  < 2e-16 ***
quarter4                   1.620e-01  5.440e-03  29.780  < 2e-16 ***
year2016                  -3.793e-02  4.696e-03  -8.079 6.94e-16 ***
year2017                   1.375e-01  4.681e-03  29.369  < 2e-16 ***
year2018                   8.566e-02  8.383e-03  10.219  < 2e-16 ***
x_large_bags               2.976e-07  2.196e-07   1.355 0.175445    
quarter2:x_large_bags      1.247e-07  2.852e-07   0.437 0.661831    
quarter3:x_large_bags      5.626e-08  2.654e-07   0.212 0.832142    
quarter4:x_large_bags      2.886e-08  4.411e-07   0.065 0.947840    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2482 on 18184 degrees of freedom
Multiple R-squared:  0.6214,    Adjusted R-squared:  0.6201 
F-statistic: 466.4 on 64 and 18184 DF,  p-value: < 2.2e-16
model5pj <- lm(average_price ~ type + region + quarter + year + x_large_bags + year:x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pj)

summary(model5pj)

Call:
lm(formula = average_price ~ type + region + quarter + year + 
    x_large_bags + year:x_large_bags, data = trimmed_avocados)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.03659 -0.14579 -0.00433  0.14385  1.44061 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                1.168e+00  1.429e-02  81.749  < 2e-16 ***
typeorganic                4.974e-01  3.764e-03 132.154  < 2e-16 ***
regionAtlanta             -2.234e-01  1.909e-02 -11.704  < 2e-16 ***
regionBaltimoreWashington -2.699e-02  1.909e-02  -1.414 0.157396    
regionBoise               -2.129e-01  1.909e-02 -11.152  < 2e-16 ***
regionBoston              -3.020e-02  1.909e-02  -1.582 0.113661    
regionBuffaloRochester    -4.425e-02  1.909e-02  -2.318 0.020447 *  
regionCalifornia          -1.711e-01  1.919e-02  -8.919  < 2e-16 ***
regionCharlotte            4.496e-02  1.909e-02   2.356 0.018508 *  
regionChicago             -4.466e-03  1.909e-02  -0.234 0.815010    
regionCincinnatiDayton    -3.516e-01  1.909e-02 -18.420  < 2e-16 ***
regionColumbus            -3.080e-01  1.909e-02 -16.136  < 2e-16 ***
regionDallasFtWorth       -4.756e-01  1.909e-02 -24.916  < 2e-16 ***
regionDenver              -3.424e-01  1.909e-02 -17.941  < 2e-16 ***
regionDetroit             -2.846e-01  1.911e-02 -14.895  < 2e-16 ***
regionGrandRapids         -5.664e-02  1.909e-02  -2.967 0.003014 ** 
regionGreatLakes          -2.233e-01  1.934e-02 -11.543  < 2e-16 ***
regionHarrisburgScranton  -4.784e-02  1.909e-02  -2.506 0.012213 *  
regionHartfordSpringfield  2.576e-01  1.909e-02  13.494  < 2e-16 ***
regionHouston             -5.131e-01  1.909e-02 -26.880  < 2e-16 ***
regionIndianapolis        -2.468e-01  1.909e-02 -12.931  < 2e-16 ***
regionJacksonville        -5.016e-02  1.909e-02  -2.628 0.008599 ** 
regionLasVegas            -1.801e-01  1.909e-02  -9.435  < 2e-16 ***
regionLosAngeles          -3.490e-01  1.915e-02 -18.229  < 2e-16 ***
regionLouisville          -2.742e-01  1.909e-02 -14.368  < 2e-16 ***
regionMiamiFtLauderdale   -1.328e-01  1.909e-02  -6.959 3.55e-12 ***
regionMidsouth            -1.574e-01  1.909e-02  -8.244  < 2e-16 ***
regionNashville           -3.490e-01  1.909e-02 -18.284  < 2e-16 ***
regionNewOrleansMobile    -2.568e-01  1.909e-02 -13.454  < 2e-16 ***
regionNewYork              1.661e-01  1.909e-02   8.703  < 2e-16 ***
regionNortheast            3.946e-02  1.909e-02   2.067 0.038749 *  
regionNorthernNewEngland  -8.372e-02  1.909e-02  -4.386 1.16e-05 ***
regionOrlando             -5.503e-02  1.909e-02  -2.883 0.003940 ** 
regionPhiladelphia         7.103e-02  1.909e-02   3.721 0.000199 ***
regionPhoenixTucson       -3.367e-01  1.909e-02 -17.642  < 2e-16 ***
regionPittsburgh          -1.967e-01  1.909e-02 -10.307  < 2e-16 ***
regionPlains              -1.253e-01  1.909e-02  -6.565 5.33e-11 ***
regionPortland            -2.433e-01  1.909e-02 -12.745  < 2e-16 ***
regionRaleighGreensboro   -5.975e-03  1.909e-02  -0.313 0.754243    
regionRichmondNorfolk     -2.698e-01  1.909e-02 -14.135  < 2e-16 ***
regionRoanoke             -3.131e-01  1.909e-02 -16.406  < 2e-16 ***
regionSacramento           6.033e-02  1.909e-02   3.161 0.001576 ** 
regionSanDiego            -1.630e-01  1.909e-02  -8.539  < 2e-16 ***
regionSanFrancisco         2.430e-01  1.909e-02  12.729  < 2e-16 ***
regionSeattle             -1.185e-01  1.909e-02  -6.207 5.53e-10 ***
regionSouthCarolina       -1.580e-01  1.909e-02  -8.278  < 2e-16 ***
regionSouthCentral        -4.616e-01  1.911e-02 -24.147  < 2e-16 ***
regionSoutheast           -1.660e-01  1.911e-02  -8.687  < 2e-16 ***
regionSpokane             -1.154e-01  1.909e-02  -6.046 1.51e-09 ***
regionStLouis             -1.306e-01  1.909e-02  -6.842 8.07e-12 ***
regionSyracuse            -4.071e-02  1.909e-02  -2.133 0.032948 *  
regionTampa               -1.524e-01  1.909e-02  -7.984 1.50e-15 ***
regionTotalUS             -2.574e-01  2.084e-02 -12.350  < 2e-16 ***
regionWest                -2.895e-01  1.909e-02 -15.163  < 2e-16 ***
regionWestTexNewMexico    -2.967e-01  1.913e-02 -15.509  < 2e-16 ***
quarter2                   8.056e-02  5.411e-03  14.887  < 2e-16 ***
quarter3                   2.183e-01  5.415e-03  40.325  < 2e-16 ***
quarter4                   1.626e-01  5.378e-03  30.244  < 2e-16 ***
year2016                  -3.908e-02  4.749e-03  -8.229  < 2e-16 ***
year2017                   1.354e-01  4.739e-03  28.580  < 2e-16 ***
year2018                   8.441e-02  8.477e-03   9.957  < 2e-16 ***
x_large_bags              -1.140e-06  5.468e-07  -2.085 0.037091 *  
year2016:x_large_bags      1.419e-06  5.571e-07   2.547 0.010880 *  
year2017:x_large_bags      1.642e-06  5.537e-07   2.966 0.003023 ** 
year2018:x_large_bags      1.461e-06  5.948e-07   2.456 0.014054 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2481 on 18184 degrees of freedom
Multiple R-squared:  0.6216,    Adjusted R-squared:  0.6203 
F-statistic: 466.8 on 64 and 18184 DF,  p-value: < 2.2e-16

So it looks like model5pa with the type, region, quarter, year, x_large_bags and type:region is the best, with a moderate gain in multiple-r2 due to the interaction. However, we need to test for the significance of the interaction given the various p-values of the associated coefficients

anova(model5, model5pa)
Analysis of Variance Table

Model 1: average_price ~ type + region + quarter + year + x_large_bags
Model 2: average_price ~ type + region + quarter + year + x_large_bags + 
    type:region
  Res.Df    RSS Df Sum of Sq     F    Pr(>F)    
1  18187 1120.1                                 
2  18134 1002.7 53    117.43 40.07 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Neat, it looks like including the interaction is statistically justified.

Automated approach

# we're putting set.seed() in here for reproducibility, but you shouldn't include
# this in production code
set.seed(42)
n_data <- nrow(trimmed_avocados)
test_index <- sample(1:n_data, size = n_data * 0.2)

test  <- slice(trimmed_avocados, test_index)
train <- slice(trimmed_avocados, -test_index)

# sanity check
nrow(test) + nrow(train) == n_data
[1] TRUE
nrow(test)
[1] 3649
nrow(train)
[1] 14600
glmulti_fit <- glmulti(
  average_price ~ ., 
  data = train,
  level = 1, # 2 = include pairwise interactions, 1 = main effects only (main effect = no pairwise interactions)
  minsize = 1, # no min size of model
  maxsize = -1, # -1 = no max size of model
  marginality = TRUE, # marginality here means the same as 'strongly hierarchical' interactions, i.e. include pairwise interactions only if both predictors present in the model as main effects.
  method = "h", # try exhaustive search, or could use "g" for genetic algorithm instead
  crit = bic, # criteria for model selection is BIC value (lower is better)
  plotty = FALSE, # don't plot models as function runs
  report = TRUE, # do produce reports as function runs
  confsetsize = 10, # return best 10 solutions
  fitfunction = lm # fit using the `lm` function
)
Initialization...
TASK: Exhaustive screening of candidate set.
Fitting...

After 50 models:
Best model: average_price~1+total_volume+x4225+x4770+small_bags
Crit= 14290.9309630974
Mean crit= 14302.7404848229

After 100 models:
Best model: average_price~1+total_volume+x4046+x4770+large_bags
Crit= 14287.0201451487
Mean crit= 14295.0164087599

After 150 models:
Best model: average_price~1+x4046+x4225+x4770+x_large_bags
Crit= 14282.9391871136
Mean crit= 14288.655212267

After 200 models:
Best model: average_price~1+total_volume+x4225+x4770+small_bags+x_large_bags
Crit= 14279.4193694914
Mean crit= 14287.2170591254

After 250 models:
Best model: average_price~1+total_volume+x4225+x4770+small_bags+x_large_bags
Crit= 14279.4193694914
Mean crit= 14285.8311251354

After 300 models:
Best model: average_price~1+x4225+region
Crit= 11937.9201055248
Mean crit= 11948.2560227565

After 350 models:
Best model: average_price~1+x4225+region
Crit= 11937.9201055248
Mean crit= 11946.7914993621

After 400 models:
Best model: average_price~1+total_volume+x4046+x_large_bags+region
Crit= 11925.5711979638
Mean crit= 11936.6091736735

After 450 models:
Best model: average_price~1+total_volume+x4225+x_large_bags+region
Crit= 11921.550556659
Mean crit= 11926.6655997315

After 500 models:
Best model: average_price~1+total_volume+x4225+x_large_bags+region
Crit= 11921.550556659
Mean crit= 11926.6075265317

After 550 models:
Best model: average_price~1+type+x4046+x4225+x4770
Crit= 7734.8593327961
Mean crit= 7793.00094370359

After 600 models:
Best model: average_price~1+type+total_volume+x4225+x4770+small_bags
Crit= 7697.79186941605
Mean crit= 7707.77632276868

After 650 models:
Best model: average_price~1+type+total_volume+x4046+x4225+x4770+small_bags+large_bags
Crit= 7665.37294598611
Mean crit= 7691.99478130502

After 700 models:
Best model: average_price~1+type+total_volume+x4046+x4225+total_bags+small_bags+large_bags
Crit= 7665.32155031575
Mean crit= 7671.67032729922

After 750 models:
Best model: average_price~1+type+total_volume+x4225+x4770+small_bags+x_large_bags
Crit= 7657.97738881932
Mean crit= 7664.22564265621

After 800 models:
Best model: average_price~1+type+total_volume+x4225+region
Crit= 3977.52101108293
Mean crit= 5088.37870955926

After 850 models:
Best model: average_price~1+type+total_volume+small_bags+region
Crit= 3964.67515907674
Mean crit= 3970.85743694413

After 900 models:
Best model: average_price~1+type+total_volume+small_bags+region
Crit= 3964.67515907674
Mean crit= 3969.31227685631

After 950 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3925.01550491875

After 1000 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.49480426776

After 1050 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1100 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1150 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1200 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1250 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1300 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1350 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1400 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1450 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1500 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1550 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1600 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1650 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1700 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1750 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1800 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1850 models:
Best model: average_price~1+type+x4225+x_large_bags+region
Crit= 3918.18091232781
Mean crit= 3924.14806552202

After 1900 models:
Best model: average_price~1+type+year+x4225+region
Crit= 2782.77393470439
Mean crit= 2786.76963771313

After 1950 models:
Best model: average_price~1+type+year+x4225+region
Crit= 2782.77393470439
Mean crit= 2785.83493132762

After 2000 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2749.79339051662

After 2050 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2747.16085350457

After 2100 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2745.77695032743

After 2150 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2745.77695032743

After 2200 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2745.77695032743

After 2250 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2745.77695032743

After 2300 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2745.77695032743

After 2350 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2745.77695032743

After 2400 models:
Best model: average_price~1+type+year+total_volume+x_large_bags+region
Crit= 2740.75749578209
Mean crit= 2745.77695032743
summary(glmulti_fit)

So the lowest BIC model with main effects is average_price ~ type + year + quarter + total_volume + x_large_bags + region. Let’s have a look at possible extensions to this. We’re going to deliberately try to go to the point where models start to overfit (as tested by the RMSE on the test set), so we’ve seen what this looks like.

results <- tibble(
  name = c(), bic = c(), rmse_train = c(), rmse_test = c()
)
# lowest BIC model with main effects
lowest_bic_model <- lm(average_price ~ type + year + quarter + total_volume + x_large_bags + region, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "lowest bic", 
      bic = bic(lowest_bic_model),
      rmse_train = rmse(lowest_bic_model, train),
      rmse_test = rmse(lowest_bic_model, test)
    )
  )

# try adding in all possible pairs with these main effects
lowest_bic_model_all_pairs <- lm(average_price ~ (type + year + quarter + total_volume + x_large_bags + region)^2, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "lowest bic all pairs", 
      bic = bic(lowest_bic_model_all_pairs),
      rmse_train = rmse(lowest_bic_model_all_pairs, train),
      rmse_test = rmse(lowest_bic_model_all_pairs, test)
    )
  )
# try a model with all main effects
model_all_mains <- lm(average_price ~ ., data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "all mains", 
      bic = bic(model_all_mains),
      rmse_train = rmse(model_all_mains, train),
      rmse_test = rmse(model_all_mains, test)
    )
  )

# try a model with all main effects and all pairs
model_all_pairs <- lm(average_price ~ .^2, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "all pairs", 
      bic = bic(model_all_pairs),
      rmse_train = rmse(model_all_pairs, train),
      rmse_test = rmse(model_all_pairs, test)
    )
  )
# try a model with all main effects, all pairs and one triple (this is getting silly)
model_all_pairs_one_triple <- lm(average_price ~ .^2 + region:type:year, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "all pairs one triple",
      bic = bic(model_all_pairs_one_triple),
      rmse_train = rmse(model_all_pairs_one_triple, train),
      rmse_test = rmse(model_all_pairs_one_triple, test)
    )
  )
# try a model with all main effects, all pairs and multiple triples (more silly)
model_all_pairs_multi_triples <- lm(average_price ~ .^2 + region:type:year + region:type:quarter + region:year:quarter, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "all pairs multi triples",
      bic = bic(model_all_pairs_multi_triples),
      rmse_train = rmse(model_all_pairs_multi_triples, train),
      rmse_test = rmse(model_all_pairs_multi_triples, test)
    )
  )
results <- results %>%
  pivot_longer(cols = bic:rmse_test, names_to = "measure", values_to = "value") %>%
  mutate(
    name = fct_relevel(
      as_factor(name),
      "lowest bic", "all mains", "lowest bic all pairs", "all pairs", "all pairs one triple", "all pairs multi triples"
    )
  )
results %>%
  filter(measure == "bic") %>%
  ggplot(aes(x = name, y = value)) +
  geom_col(fill = "steelblue", alpha = 0.7) +
  labs(
    x = "model",
    y = "bic"
  ) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  geom_hline(aes(yintercept = 0))

BIC is telling us here that if we took our main effects model with lowest BIC, and added in all possible pairs, this would likely still improve the model for predictive purposes. BIC suggests that this ‘lowest BIC all pairs’ model will offer best predictive performance without overfitting, with all other models being significantly poorer.

results %>%
  filter(measure != "bic") %>%
  ggplot(aes(x = name, y = value, fill = measure)) +
  geom_col(position = "dodge", alpha = 0.7) +
  labs(
    x = "model",
    y = "rmse"
  ) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Lowest RMSE in test is obtained for the ‘lowest bic all pairs’ model, and it increases thereafter for the more complex models, which suggests that these models are overfitting the training data.

---
title: "R Notebook"
output: html_notebook
---

```{r}
install.packages("HH")
```

```{r}
install.packages("bestNormalize")
```

```{r}
library(HH)
library(GGally)
library(bestNormalize)
library(dplyr)
library(janitor)
library(leaps)
library(tidyverse)
library(dplyr)
library(modelr)
```

```{r}
install.packages("glmulti")
```

```{r}
library(glmulti)
```

```{r}
avacado <- read.csv("data/avocado.csv") %>% clean_names()
```

```{r}
head(avacado)
```


```{r}
avacado2 <- avacado %>% 
    dplyr::select(-c("date", "region", "x"))
```

```{r}
head(avacado2)
```

```{r}
regsubsets_forward <- regsubsets(average_price ~ ., data = avacado2, nvmax = 10, method = "forward")
```


```{r}
sum_regsubsets_forward <- summary(regsubsets_forward)
sum_regsubsets_forward
```

The best predictor model shows us the best predictors using the asterices

```{r}
# plotting this shows us the adjusted r2 values and which variables are in the model. Top row shows model with highest adjusted r2
plot(regsubsets_forward, scale = "adjr2")
```


```{r}
sum_regsubsets_forward$which
```

```{r}
regsubsets_backward <- regsubsets(average_price ~ ., data = avacado2, nvmax = 10, method = "backward")
```

```{r}

# plotting this shows us the adjusted r2 values and which variables are in the model. Top row shows model with highest adjusted r2
plot(regsubsets_backward, scale = "adjr2")
```


```{r}
regsubsets_exhaustive <- regsubsets(average_price ~ ., data = avacado2, nvmax = 10, method = "exhaustive")
```

```{r}

# plotting this shows us the adjusted r2 values and which variables are in the model. Top row shows model with highest adjusted r2
plot(regsubsets_exhaustive, scale = "adjr2")
```


```{r}
summary(regsubsets_exhaustive)$which[10,]
```


```{r}
summary(regsubsets_backward)$which[10,]
```

```{r}
summary(regsubsets_forward)$which[10,]
```


```{r}
avacado2 %>%
  ggplot(aes(x = average_price)) +
  geom_histogram()
```

```{r}
avacado2 %>%
  ggplot(aes(x = log10(average_price))) +
  geom_histogram()
```


CODECLAN- SOLUTION

```{r}
avocados <- clean_names(read_csv("data/avocado.csv"))
```

```{r}

summary(avocados)

```

```{r}
head(avocados)
```

```{r}
avocados %>%
  distinct(region) %>%
  summarise(number_of_regions = n())
```

```{r}
avocados %>%
  distinct(date) %>%
  summarise(
    number_of_dates = n(),
    min_date = min(date),
    max_date = max(date)
  )

```

```{r}
library(lubridate)
```

```{r}
trimmed_avocados <- avocados %>%
  mutate(
    quarter = as_factor(quarter(date)),
    year = as_factor(year),
    type = as_factor(type)
  ) %>%
  dplyr::select(-c("x1", "date"))
```

```{r}
alias(average_price ~ ., data = trimmed_avocados )
```

```{r}
trimmed_avocados %>%
  dplyr::select(-region) %>%
  ggpairs()
```


```{r}
ggsave("pairs_plot_choice1.png", width = 10, height = 10, units = "in")
```


```{r}
trimmed_avocados %>%
  ggplot(aes(x = region, y = average_price)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))
```

Test competing models with x4046, type, year, quarter and region:

```{r}
model1a <- lm(average_price ~ x4046, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1a)
```

```{r}
summary(model1a)
```

```{r}
model1b <- lm(average_price ~ type, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1b)
```

```{r}
summary(model1b)
```


```{r}
model1c <- lm(average_price ~ year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1c)
```

```{r}
summary(model1c)
```

```{r}
model1d <- lm(average_price ~ quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1d)
```

```{r}
summary(model1d)
```

```{r}
model1e <- lm(average_price ~ region, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model1e)

```

```{r}
summary(model1e)
```

model1b with type is best, so we’ll keep that and re-run ggpairs() with the residuals (again omitting region).


```{r}
avocados_remaining_resid <- trimmed_avocados %>%
  add_residuals(model1b) %>%
  dplyr::select(-c("average_price", "type", "region"))

ggpairs(avocados_remaining_resid)
```

```{r}
ggsave("pairs_plot_choice2.png", width = 10, height = 10, units = "in")
```


```{r}
trimmed_avocados %>%
  add_residuals(model1b) %>%
  ggplot(aes(x = region, y = resid)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))
```

Looks like x4046, year, quarter and region are our next strong contenders:

```{r}
model2a <- lm(average_price ~ type + x4046, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model2a)
```

```{r}
summary(model2a)
```

```{r}
model2b <- lm(average_price ~ type + year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model2b)
```

```{r}
summary(model2b)
```

```{r}
model2c <- lm(average_price ~ type + quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model2c)
```


```{r}
summary(model2c)

```

```{r}
model2d <- lm(average_price ~ type + region, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model2d)
```

```{r}
summary(model2d)
```

So model2d with type and region comes out as better here. We have some region coefficients that are not significant at 0.05 level, so let’s run an anova() to test whether to include region

```{r}
anova(model1b, model2d)
```

It seems region is significant overall, so we’ll keep it in!

```{r}
avocados_remaining_resid <- trimmed_avocados %>%
  add_residuals(model2d) %>%
  dplyr::select(-c("average_price", "type", "region"))

ggpairs(avocados_remaining_resid)
```


```{r}
ggsave("pairs_plot_choice3.png", width = 10, height = 10, units = "in")
```


```{r}
model3a <- lm(average_price ~ type + region + x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model3a)
```


```{r}
summary(model3a)
```


```{r}
model3b <- lm(average_price ~ type + region + year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model3b)
```


```{r}
summary(model3b)
```



```{r}
model3c <- lm(average_price ~ type + region + quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model3c)
```

```{r}
summary(model3c)
```

So model3c with type, region and quarter wins out here. Everything still looks reasonable with the diagnostics, perhaps some mild heteroscedasticity.

```{r}
avocados_remaining_resid <- trimmed_avocados %>%
  add_residuals(model3c) %>%
  dplyr::select(-c("average_price", "type", "region", "quarter"))

ggpairs(avocados_remaining_resid)
```


```{r}
ggsave("pairs_plot_choice4.png", width = 10, height = 10, units = "in")

```

```{r}
model4a <- lm(average_price ~ type + region + quarter + x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model4a)
```

```{r}
summary(model4a)
```

```{r}
model4b <- lm(average_price ~ type + region + quarter + year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model4b)
```

```{r}
summary(model4b)
```

Hmm, model4b with type, region, quarter and year wins here

```{r}
avocados_remaining_resid <- trimmed_avocados %>%
  add_residuals(model4b) %>%
  dplyr::select(-c("average_price", "type", "region", "quarter", "year"))

ggpairs(avocados_remaining_resid)
```

```{r}
ggsave("pairs_plot_choice5.png", width = 10, height = 10, units = "in")
```

It looks like x_large_bags is the remaining contender, let’s check it out!

```{r}
model5 <- lm(average_price ~ type + region + quarter + year + x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5)
```

```{r}
summary(model5)
```

It is a significant explanatory variable, so let’s keep it. Overall, we still have some heterscedasticity and deviations from normality in the residuals.


Let’s now think about possible pair interactions: for five main effect variables we have ten possible pair interactions. Let’s test them out.

```{r}
model5pa <- lm(average_price ~ type + region + quarter + year + x_large_bags + type:region, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pa)
```

```{r}
summary(model5pa)
```


```{r}
model5pb <- lm(average_price ~ type + region + quarter + year + x_large_bags + type:quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pb)
```

```{r}
summary(model5pb)
```

```{r}
model5pc <- lm(average_price ~ type + region + quarter + year + x_large_bags + type:year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pc)
```

```{r}
summary(model5pc)
```

```{r}
model5pd <- lm(average_price ~ type + region + quarter + year + x_large_bags + type:x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pd)
```

```{r}
summary(model5pd)
```


```{r}
model5pe <- lm(average_price ~ type + region + quarter + year + x_large_bags + region:quarter, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pe)
```


```{r}
summary(model5pe)
```

```{r}

model5pf <- lm(average_price ~ type + region + quarter + year + x_large_bags + region:year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pf)
```

```{r}
summary(model5pf)
```

```{r}
model5pg <- lm(average_price ~ type + region + quarter + year + x_large_bags + region:x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pg)
```

```{r}
summary(model5pg)
```

```{r}
model5ph <- lm(average_price ~ type + region + quarter + year + x_large_bags + quarter:year, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5ph)
```

```{r}
summary(model5ph)
```

```{r}
model5pi <- lm(average_price ~ type + region + quarter + year + x_large_bags + quarter:x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pi)
```

```{r}
summary(model5pi)
```

```{r}
model5pj <- lm(average_price ~ type + region + quarter + year + x_large_bags + year:x_large_bags, data = trimmed_avocados)
par(mfrow = c(2, 2))
plot(model5pj)
```

```{r}
summary(model5pj)
```


So it looks like model5pa with the type, region, quarter, year, x_large_bags and type:region is the best, with a moderate gain in multiple-r2 due to the interaction. However, we need to test for the significance of the interaction given the various p-values of the associated coefficients

```{r}
anova(model5, model5pa)
```

Neat, it looks like including the interaction is statistically justified.

Automated approach
```{r}
# we're putting set.seed() in here for reproducibility, but you shouldn't include
# this in production code
set.seed(42)
n_data <- nrow(trimmed_avocados)
test_index <- sample(1:n_data, size = n_data * 0.2)

test  <- slice(trimmed_avocados, test_index)
train <- slice(trimmed_avocados, -test_index)

# sanity check
nrow(test) + nrow(train) == n_data
```

```{r}
nrow(test)

```

```{r}
nrow(train)
```

```{r}
glmulti_fit <- glmulti(
  average_price ~ ., 
  data = train,
  level = 1, # 2 = include pairwise interactions, 1 = main effects only (main effect = no pairwise interactions)
  minsize = 1, # no min size of model
  maxsize = -1, # -1 = no max size of model
  marginality = TRUE, # marginality here means the same as 'strongly hierarchical' interactions, i.e. include pairwise interactions only if both predictors present in the model as main effects.
  method = "h", # try exhaustive search, or could use "g" for genetic algorithm instead
  crit = bic, # criteria for model selection is BIC value (lower is better)
  plotty = FALSE, # don't plot models as function runs
  report = TRUE, # do produce reports as function runs
  confsetsize = 10, # return best 10 solutions
  fitfunction = lm # fit using the `lm` function
)
```

```{r}
summary(glmulti_fit)
```

So the lowest BIC model with main effects is average_price ~ type + year + quarter + total_volume + x_large_bags + region. Let’s have a look at possible extensions to this. We’re going to deliberately try to go to the point where models start to overfit (as tested by the RMSE on the test set), so we’ve seen what this looks like.
```{r}
results <- tibble(
  name = c(), bic = c(), rmse_train = c(), rmse_test = c()
)
```

```{r}
# lowest BIC model with main effects
lowest_bic_model <- lm(average_price ~ type + year + quarter + total_volume + x_large_bags + region, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "lowest bic", 
      bic = bic(lowest_bic_model),
      rmse_train = rmse(lowest_bic_model, train),
      rmse_test = rmse(lowest_bic_model, test)
    )
  )

# try adding in all possible pairs with these main effects
lowest_bic_model_all_pairs <- lm(average_price ~ (type + year + quarter + total_volume + x_large_bags + region)^2, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "lowest bic all pairs", 
      bic = bic(lowest_bic_model_all_pairs),
      rmse_train = rmse(lowest_bic_model_all_pairs, train),
      rmse_test = rmse(lowest_bic_model_all_pairs, test)
    )
  )
```

```{r}
# try a model with all main effects
model_all_mains <- lm(average_price ~ ., data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "all mains", 
      bic = bic(model_all_mains),
      rmse_train = rmse(model_all_mains, train),
      rmse_test = rmse(model_all_mains, test)
    )
  )

# try a model with all main effects and all pairs
model_all_pairs <- lm(average_price ~ .^2, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "all pairs", 
      bic = bic(model_all_pairs),
      rmse_train = rmse(model_all_pairs, train),
      rmse_test = rmse(model_all_pairs, test)
    )
  )
```

```{r}
# try a model with all main effects, all pairs and one triple (this is getting silly)
model_all_pairs_one_triple <- lm(average_price ~ .^2 + region:type:year, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "all pairs one triple",
      bic = bic(model_all_pairs_one_triple),
      rmse_train = rmse(model_all_pairs_one_triple, train),
      rmse_test = rmse(model_all_pairs_one_triple, test)
    )
  )
```

```{r}
# try a model with all main effects, all pairs and multiple triples (more silly)
model_all_pairs_multi_triples <- lm(average_price ~ .^2 + region:type:year + region:type:quarter + region:year:quarter, data = train)
results <- results %>%
  add_row(
    tibble_row(
      name = "all pairs multi triples",
      bic = bic(model_all_pairs_multi_triples),
      rmse_train = rmse(model_all_pairs_multi_triples, train),
      rmse_test = rmse(model_all_pairs_multi_triples, test)
    )
  )
```

```{r}
results <- results %>%
  pivot_longer(cols = bic:rmse_test, names_to = "measure", values_to = "value") %>%
  mutate(
    name = fct_relevel(
      as_factor(name),
      "lowest bic", "all mains", "lowest bic all pairs", "all pairs", "all pairs one triple", "all pairs multi triples"
    )
  )
```


```{r}
results %>%
  filter(measure == "bic") %>%
  ggplot(aes(x = name, y = value)) +
  geom_col(fill = "steelblue", alpha = 0.7) +
  labs(
    x = "model",
    y = "bic"
  ) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  geom_hline(aes(yintercept = 0))
```

BIC is telling us here that if we took our main effects model with lowest BIC, and added in all possible pairs, this would likely still improve the model for predictive purposes. BIC suggests that this ‘lowest BIC all pairs’ model will offer best predictive performance without overfitting, with all other models being significantly poorer.

```{r}
results %>%
  filter(measure != "bic") %>%
  ggplot(aes(x = name, y = value, fill = measure)) +
  geom_col(position = "dodge", alpha = 0.7) +
  labs(
    x = "model",
    y = "rmse"
  ) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))
```


Lowest RMSE in test is obtained for the ‘lowest bic all pairs’ model, and it increases thereafter for the more complex models, which suggests that these models are overfitting the training data.